Month: February 2026
Microsoft and OpenAI joint statement on continuing partnership
Since 2019, Microsoft and OpenAI have worked together to advance artificial intelligence responsibly and make its benefits broadly accessible. What began as a research partnership has grown into one of the most consequential collaborations in technology — grounded in mutual trust, deep technical integration, and a long‑term commitment to innovation.
As conversations around AI investments and partnerships grow and as OAI announces new funding and new partners as they did today, we want to ensure these announcements are understood within the existing construct of our partnership. Nothing about today’s announcements in any way changes the terms of the Microsoft and OpenAI relationship that have been previously shared in our joint blog in October 2025.
The partnership remains strong and central. Microsoft and OpenAI continue to work closely across research, engineering, and product development, building on years of deep collaboration and shared success.
Our IP relationship continues unchanged. Microsoft maintains its exclusive license and access to intellectual property across OpenAI models and products. Collaborations like the partnership between OpenAI and Amazon were always contemplated under our agreements and Microsoft is excited to see what they build together.
Our commercial and revenue share relationship remains unchanged. The ongoing revenue share arrangement remains unchanged and has always included sharing revenue from partnerships between OpenAI and other cloud providers.
Azure remains the exclusive cloud provider of stateless OpenAI APIs. Microsoft is the exclusive cloud provider for stateless APIs that provide access to OpenAI’s models and IP. These APIs can be purchased from Microsoft or directly from OpenAI. Customers and developers benefit from Azure’s global infrastructure, security, and enterprise-grade capabilities at scale. Any stateless API calls to OpenAI models that result from a collaboration between OpenAI and any third party – including Amazon – would be hosted on Azure.
OpenAI’s first party products, including Frontier, will continue to be hosted on Azure.
AGI definition and processes are unchanged. The contractual definition of AGI and the process for determining if it has been achieved remains the same.
The partnership supports OpenAI’s growth. As OpenAI scales, it continues to have flexibility to commit to additional compute elsewhere, including through large-scale infrastructure initiatives such as the Stargate project.
The partnership was designed to give Microsoft and OpenAI room to pursue new opportunities independently, while continuing to collaborate, which each company is doing, together and independently.
We remain committed to our partnership and to the shared mission that brought us together. We continue to work side‑by‑side to deliver powerful AI tools, advance responsible development, and ensure that AI benefits people and organizations everywhere.
The post Microsoft and OpenAI joint statement on continuing partnership appeared first on The Official Microsoft Blog.
Since 2019, Microsoft and OpenAI have worked together to advance artificial intelligence responsibly and make its benefits broadly accessible. What began as a research partnership has grown into one of the most consequential collaborations in technology — grounded in mutual trust, deep technical integration, and a long‑term commitment to innovation. As conversations around AI investments and partnerships…
The post Microsoft and OpenAI joint statement on continuing partnership appeared first on The Official Microsoft Blog.Read More
Have installed Matlab 2025b on my Macbook air M2 but it crashes at startup. Have tried a new installation but didn’t work.
Hello there, I need help installing matlab 2025b on my macbook running Tahoe 26.1. The instalation runs smothly but once instaled, Matlab crashes at startup. I have erased and tried a fresh instalation but have not worked. What would you suggest me to do?
Yours sincerely,
DanielHello there, I need help installing matlab 2025b on my macbook running Tahoe 26.1. The instalation runs smothly but once instaled, Matlab crashes at startup. I have erased and tried a fresh instalation but have not worked. What would you suggest me to do?
Yours sincerely,
Daniel Hello there, I need help installing matlab 2025b on my macbook running Tahoe 26.1. The instalation runs smothly but once instaled, Matlab crashes at startup. I have erased and tried a fresh instalation but have not worked. What would you suggest me to do?
Yours sincerely,
Daniel matlab installation, mac, 2025b, tahoe, crash MATLAB Answers — New Questions
Please help me to solve this simple error in definition of dy(3)
proj()
function sol= proj
myLegend1 = {};
myLegend2 = {};
k0=386; ce=3.831*10^2;rho=89.54*10^2;alfat=1.78*10^-5;taw=0.5;Tnot=2.93*10^2;mu=38.6*10^5; lamda=77.6*10^5;
%lamda=77.6e^9;
%mu=38.6*e^9;lamda=77.6e+9
c0=sqrt((lamda+2*mu)/(rho)); Betanot=(3*lamda+2*mu)*alfat; a1=mu/(lamda+2*mu);a2=(mu+lamda)/(lamda+2*mu);a3=(Betanot*Tnot)/(lamda+2*mu);omega=(rho*ce)/(k0);
a4=lamda/(lamda+2*mu);a5=(k0*omega*c0^2)/(k0);a6=(rho*ce*c0^2)/(k0);
a7=(Betanot*c0^2)/(k0); a8=a6*taw; a9=a7*taw; a10=rho*ce*taw*omega*c0^4/(k0); a11=Betanot*taw*omega*c0^4/(k0);w=rho*ce/(k0);
rr = [0.3 ];
for i =1:numel(rr)
a= rr(i);
s=0.01;h=0.01;b=0.01;
y0 = [0,0,0,0,0,0,1,0,0];
disp(a7)
options =bvpset(‘stats’,’on’,’RelTol’,1e-4);
m = linspace(0,2);
solinit = bvpinit(m,y0);
sol= bvp4c(@projfun,@projbc,solinit,options);
figure(1)
plot(sol.x,abs(sol.y(1,:)))
grid on,hold on
myLegend1{i}=[‘alfa= ‘,num2str(rr(i))];
figure(2)
plot(sol.x,(sol.y(7,:)))
title(‘Temperature’)
grid on,hold on
myLegend2{i}=[‘alfa= ‘,num2str(rr(i))];
i=i+1;
end
figure(1)
legend(myLegend1)
hold on
figure(2)
legend(myLegend2)
function dy = projfun(x,y)
dy = zeros(9,1);
E = y(1);
dE = y(2);
ddE=y(3);
u = y(4);
du = y(5);
ddu=y(6);
t = y(7);
dt = y(8);
ddt=y(9);
dy(1) = dE;
dy(2)=(1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du));
dy(3)=((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2)^2))*(((((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2)))*((a2*s*h-a*a2*s*h*t)*(2*a*a3*s*(t*ddt+dt*dt)+2*a*a3*t*dt-a3*s*ddt-a3*dt-a*(a4*(s+h)+a1*(s+h))*dt*dE-a*(s^2+a1*h^2)*(dt*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))+dt*dE)))+(a2*(s+h)-a*a2*s*h*dt-a*a2*(s+h)*t)*(2*a*a3*s*t*dt-a3*s*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)-(s^2+a1*h^2-(x+b+1))*(1-a*t)*((2*a*a3*h)*(t*ddt+dt*dt)+2*a*a3*t*dt-a3*dt-ddt*a3*h-a*(a4+a1)*(s+h)*dt*du-a*(h^2+a1*s^2)*(dt*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))+ddt*dE)-a*2*(h+s)*dt*dE-a*s*h*(a4+a1)*(dt*((1/((a*(s^2+a1*h^2-(x+b+1)^2)*t-(s^2+a1*h^2-(x+b+1)^2))))*((-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)+(a2*s*h-a*a2*s*h*t)*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-1*a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))))+dt*du)-(2*a*a3*s*t*dt-a3*s*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)*(2*s+2*a1*h-a*(s^2+a1*h^2-(x+b+1)^2)*dt-(2*a*(s+a1*h))*t))-((a2*s*h-a*a2*s*h*t)*(2*a*a3*s*t*dt-a3*s*dt-a*(s^2+a1*h^2)*dt*du-a*(a*s*h*(a4+a1))*dt*dE)-(s^2+a1*h^2-(x+b+1)^2)*(1-a*t)*(2*a*a3*h*t*dt-a3*h*dt-a*(s^2+a1*h^2)*dt*dE-a*s*h*(a4+a1)*dt*du))*((s^2+a1*h^2-(x+b+1)^2)*2*(h+a1*s)+2*(s+a1*h)*(h^2+a1*s^2-(x+b+1)^2)+2*a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2)*t*dt+t^2*(a*(s^2+a1*h^2-(x+b+1)^2)*a*2*(h+a1*s)+a*2*(s+a1*h)*a*(h^2+a1*s^2-(x+b+1)^2))-t*((s^2+a1*h^2-(x+b+1)^2)*a*2*(h+s*a1)+2*(s+a1*h)*a*(h^2+a1*s^2-(x+b+1)^2)+a*(s^2+a1*h^2-(x+b+1)^2)*2*(h+a1*s)+a*2*(s+a1*h)*(h^2+a1*s^2-(x+b+1)^2))-2*a2*s*h(1-a*t)*(a2*(s+h)-a*a2*s*h*dt-a*a2*(s+h)*t)-dt*(a*(s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))));
dy(4)=du;
dy(5)=(1/((a*(s^2+a1*h^2-(x+b+1)^2)*t-(s^2+a1*h^2-(x+b+1)^2))))*((-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)+(a2*s*h-a*a2*s*h*t)*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du))));
dy(6) =(1/((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t))*((a2*s*h-(a*a2*s*h)*t)*((1/((((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t)*(((s^2+a1*h^2-(x+b+1).^2))-a*(s^2+a1*h^2-(x+b+1)*(x+b+1))*t))-(a2*s*h-(a*a2*s*h)*t)^2))*((a2*s*h-(a*a2*s*h)*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)-(((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t))*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*s*h*(a4+a1)*dt*du)))+(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE));
dy(7)=dt;
dy(8)=ddt;
dy(9)=(1/((a*(x+b+1)*(a5*(s^2+h^2)-a8*(x+b+1)*(x+b+1)))*t-((x+b+1)*(a5*s^2+a5*h^2-a8*(x+b+1)*(x+b+1)))))*((s^2+h^2+2*a5*s*+2*a5*h-a6*(x+b+1)*(x+b+1))*ddt+((2*a*a7*(x+b+1))*t-2*(x+b+1)*(a7-a*a11))*((1/((((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t)*(((s^2+a1*h^2-(x+b+1)*(x+b+1)))-a*(s^2+a1*h^2-(x+b+1)*(x+b+1))*t))-(a2*s*h-(a*a2*s*h)*t)^2))*((a2*s*h-(a*a2*s*h)*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)-(((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t))*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*s*h*(a4+a1)*dt*du)))+((a*2*a7)*t-(2*(x+b+1)*(a7-2*a*a11)))*((1/((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t))*((a2*s*h-(a*a2*s*h)*t)*((1/((((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t)*(((s^2+a1*h^2-(x+b+1)*(x+b+1)))-a*(s^2+a1*h^2-(x+b+1)*(x+b+1))*t))-(a2*s*h-(a*a2*s*h)*t)^2))*((a2*s*h-(a*a2*s*h)*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)-(((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t))*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*s*h*(a4+a1)*dt*du)))+(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)))-a*(s^2+h^2+2*a5*s+2*a5*h-a6*(x+b+1)*(x+b+1))*t*ddt-a*(s^2+h^2+a5*s+a5*h)*dt*dt-a*(x+b+1)*(a5*s^2+a5*h^2+a10*(x+b+1)*(x+b+1))*dt*ddt);
end
function res = projbc(ya,yb)
res = [ya(1);
ya(4);
ya(7)-1;
ya(3);
ya(5);
yb(1);
yb(4);
yb(7)-0.5;
yb(9)];
end
endproj()
function sol= proj
myLegend1 = {};
myLegend2 = {};
k0=386; ce=3.831*10^2;rho=89.54*10^2;alfat=1.78*10^-5;taw=0.5;Tnot=2.93*10^2;mu=38.6*10^5; lamda=77.6*10^5;
%lamda=77.6e^9;
%mu=38.6*e^9;lamda=77.6e+9
c0=sqrt((lamda+2*mu)/(rho)); Betanot=(3*lamda+2*mu)*alfat; a1=mu/(lamda+2*mu);a2=(mu+lamda)/(lamda+2*mu);a3=(Betanot*Tnot)/(lamda+2*mu);omega=(rho*ce)/(k0);
a4=lamda/(lamda+2*mu);a5=(k0*omega*c0^2)/(k0);a6=(rho*ce*c0^2)/(k0);
a7=(Betanot*c0^2)/(k0); a8=a6*taw; a9=a7*taw; a10=rho*ce*taw*omega*c0^4/(k0); a11=Betanot*taw*omega*c0^4/(k0);w=rho*ce/(k0);
rr = [0.3 ];
for i =1:numel(rr)
a= rr(i);
s=0.01;h=0.01;b=0.01;
y0 = [0,0,0,0,0,0,1,0,0];
disp(a7)
options =bvpset(‘stats’,’on’,’RelTol’,1e-4);
m = linspace(0,2);
solinit = bvpinit(m,y0);
sol= bvp4c(@projfun,@projbc,solinit,options);
figure(1)
plot(sol.x,abs(sol.y(1,:)))
grid on,hold on
myLegend1{i}=[‘alfa= ‘,num2str(rr(i))];
figure(2)
plot(sol.x,(sol.y(7,:)))
title(‘Temperature’)
grid on,hold on
myLegend2{i}=[‘alfa= ‘,num2str(rr(i))];
i=i+1;
end
figure(1)
legend(myLegend1)
hold on
figure(2)
legend(myLegend2)
function dy = projfun(x,y)
dy = zeros(9,1);
E = y(1);
dE = y(2);
ddE=y(3);
u = y(4);
du = y(5);
ddu=y(6);
t = y(7);
dt = y(8);
ddt=y(9);
dy(1) = dE;
dy(2)=(1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du));
dy(3)=((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2)^2))*(((((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2)))*((a2*s*h-a*a2*s*h*t)*(2*a*a3*s*(t*ddt+dt*dt)+2*a*a3*t*dt-a3*s*ddt-a3*dt-a*(a4*(s+h)+a1*(s+h))*dt*dE-a*(s^2+a1*h^2)*(dt*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))+dt*dE)))+(a2*(s+h)-a*a2*s*h*dt-a*a2*(s+h)*t)*(2*a*a3*s*t*dt-a3*s*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)-(s^2+a1*h^2-(x+b+1))*(1-a*t)*((2*a*a3*h)*(t*ddt+dt*dt)+2*a*a3*t*dt-a3*dt-ddt*a3*h-a*(a4+a1)*(s+h)*dt*du-a*(h^2+a1*s^2)*(dt*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))+ddt*dE)-a*2*(h+s)*dt*dE-a*s*h*(a4+a1)*(dt*((1/((a*(s^2+a1*h^2-(x+b+1)^2)*t-(s^2+a1*h^2-(x+b+1)^2))))*((-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)+(a2*s*h-a*a2*s*h*t)*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-1*a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))))+dt*du)-(2*a*a3*s*t*dt-a3*s*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)*(2*s+2*a1*h-a*(s^2+a1*h^2-(x+b+1)^2)*dt-(2*a*(s+a1*h))*t))-((a2*s*h-a*a2*s*h*t)*(2*a*a3*s*t*dt-a3*s*dt-a*(s^2+a1*h^2)*dt*du-a*(a*s*h*(a4+a1))*dt*dE)-(s^2+a1*h^2-(x+b+1)^2)*(1-a*t)*(2*a*a3*h*t*dt-a3*h*dt-a*(s^2+a1*h^2)*dt*dE-a*s*h*(a4+a1)*dt*du))*((s^2+a1*h^2-(x+b+1)^2)*2*(h+a1*s)+2*(s+a1*h)*(h^2+a1*s^2-(x+b+1)^2)+2*a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2)*t*dt+t^2*(a*(s^2+a1*h^2-(x+b+1)^2)*a*2*(h+a1*s)+a*2*(s+a1*h)*a*(h^2+a1*s^2-(x+b+1)^2))-t*((s^2+a1*h^2-(x+b+1)^2)*a*2*(h+s*a1)+2*(s+a1*h)*a*(h^2+a1*s^2-(x+b+1)^2)+a*(s^2+a1*h^2-(x+b+1)^2)*2*(h+a1*s)+a*2*(s+a1*h)*(h^2+a1*s^2-(x+b+1)^2))-2*a2*s*h(1-a*t)*(a2*(s+h)-a*a2*s*h*dt-a*a2*(s+h)*t)-dt*(a*(s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))));
dy(4)=du;
dy(5)=(1/((a*(s^2+a1*h^2-(x+b+1)^2)*t-(s^2+a1*h^2-(x+b+1)^2))))*((-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)+(a2*s*h-a*a2*s*h*t)*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du))));
dy(6) =(1/((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t))*((a2*s*h-(a*a2*s*h)*t)*((1/((((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t)*(((s^2+a1*h^2-(x+b+1).^2))-a*(s^2+a1*h^2-(x+b+1)*(x+b+1))*t))-(a2*s*h-(a*a2*s*h)*t)^2))*((a2*s*h-(a*a2*s*h)*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)-(((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t))*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*s*h*(a4+a1)*dt*du)))+(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE));
dy(7)=dt;
dy(8)=ddt;
dy(9)=(1/((a*(x+b+1)*(a5*(s^2+h^2)-a8*(x+b+1)*(x+b+1)))*t-((x+b+1)*(a5*s^2+a5*h^2-a8*(x+b+1)*(x+b+1)))))*((s^2+h^2+2*a5*s*+2*a5*h-a6*(x+b+1)*(x+b+1))*ddt+((2*a*a7*(x+b+1))*t-2*(x+b+1)*(a7-a*a11))*((1/((((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t)*(((s^2+a1*h^2-(x+b+1)*(x+b+1)))-a*(s^2+a1*h^2-(x+b+1)*(x+b+1))*t))-(a2*s*h-(a*a2*s*h)*t)^2))*((a2*s*h-(a*a2*s*h)*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)-(((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t))*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*s*h*(a4+a1)*dt*du)))+((a*2*a7)*t-(2*(x+b+1)*(a7-2*a*a11)))*((1/((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t))*((a2*s*h-(a*a2*s*h)*t)*((1/((((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t)*(((s^2+a1*h^2-(x+b+1)*(x+b+1)))-a*(s^2+a1*h^2-(x+b+1)*(x+b+1))*t))-(a2*s*h-(a*a2*s*h)*t)^2))*((a2*s*h-(a*a2*s*h)*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)-(((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t))*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*s*h*(a4+a1)*dt*du)))+(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)))-a*(s^2+h^2+2*a5*s+2*a5*h-a6*(x+b+1)*(x+b+1))*t*ddt-a*(s^2+h^2+a5*s+a5*h)*dt*dt-a*(x+b+1)*(a5*s^2+a5*h^2+a10*(x+b+1)*(x+b+1))*dt*ddt);
end
function res = projbc(ya,yb)
res = [ya(1);
ya(4);
ya(7)-1;
ya(3);
ya(5);
yb(1);
yb(4);
yb(7)-0.5;
yb(9)];
end
end proj()
function sol= proj
myLegend1 = {};
myLegend2 = {};
k0=386; ce=3.831*10^2;rho=89.54*10^2;alfat=1.78*10^-5;taw=0.5;Tnot=2.93*10^2;mu=38.6*10^5; lamda=77.6*10^5;
%lamda=77.6e^9;
%mu=38.6*e^9;lamda=77.6e+9
c0=sqrt((lamda+2*mu)/(rho)); Betanot=(3*lamda+2*mu)*alfat; a1=mu/(lamda+2*mu);a2=(mu+lamda)/(lamda+2*mu);a3=(Betanot*Tnot)/(lamda+2*mu);omega=(rho*ce)/(k0);
a4=lamda/(lamda+2*mu);a5=(k0*omega*c0^2)/(k0);a6=(rho*ce*c0^2)/(k0);
a7=(Betanot*c0^2)/(k0); a8=a6*taw; a9=a7*taw; a10=rho*ce*taw*omega*c0^4/(k0); a11=Betanot*taw*omega*c0^4/(k0);w=rho*ce/(k0);
rr = [0.3 ];
for i =1:numel(rr)
a= rr(i);
s=0.01;h=0.01;b=0.01;
y0 = [0,0,0,0,0,0,1,0,0];
disp(a7)
options =bvpset(‘stats’,’on’,’RelTol’,1e-4);
m = linspace(0,2);
solinit = bvpinit(m,y0);
sol= bvp4c(@projfun,@projbc,solinit,options);
figure(1)
plot(sol.x,abs(sol.y(1,:)))
grid on,hold on
myLegend1{i}=[‘alfa= ‘,num2str(rr(i))];
figure(2)
plot(sol.x,(sol.y(7,:)))
title(‘Temperature’)
grid on,hold on
myLegend2{i}=[‘alfa= ‘,num2str(rr(i))];
i=i+1;
end
figure(1)
legend(myLegend1)
hold on
figure(2)
legend(myLegend2)
function dy = projfun(x,y)
dy = zeros(9,1);
E = y(1);
dE = y(2);
ddE=y(3);
u = y(4);
du = y(5);
ddu=y(6);
t = y(7);
dt = y(8);
ddt=y(9);
dy(1) = dE;
dy(2)=(1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du));
dy(3)=((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2)^2))*(((((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2)))*((a2*s*h-a*a2*s*h*t)*(2*a*a3*s*(t*ddt+dt*dt)+2*a*a3*t*dt-a3*s*ddt-a3*dt-a*(a4*(s+h)+a1*(s+h))*dt*dE-a*(s^2+a1*h^2)*(dt*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))+dt*dE)))+(a2*(s+h)-a*a2*s*h*dt-a*a2*(s+h)*t)*(2*a*a3*s*t*dt-a3*s*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)-(s^2+a1*h^2-(x+b+1))*(1-a*t)*((2*a*a3*h)*(t*ddt+dt*dt)+2*a*a3*t*dt-a3*dt-ddt*a3*h-a*(a4+a1)*(s+h)*dt*du-a*(h^2+a1*s^2)*(dt*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))+ddt*dE)-a*2*(h+s)*dt*dE-a*s*h*(a4+a1)*(dt*((1/((a*(s^2+a1*h^2-(x+b+1)^2)*t-(s^2+a1*h^2-(x+b+1)^2))))*((-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)+(a2*s*h-a*a2*s*h*t)*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-1*a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))))+dt*du)-(2*a*a3*s*t*dt-a3*s*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)*(2*s+2*a1*h-a*(s^2+a1*h^2-(x+b+1)^2)*dt-(2*a*(s+a1*h))*t))-((a2*s*h-a*a2*s*h*t)*(2*a*a3*s*t*dt-a3*s*dt-a*(s^2+a1*h^2)*dt*du-a*(a*s*h*(a4+a1))*dt*dE)-(s^2+a1*h^2-(x+b+1)^2)*(1-a*t)*(2*a*a3*h*t*dt-a3*h*dt-a*(s^2+a1*h^2)*dt*dE-a*s*h*(a4+a1)*dt*du))*((s^2+a1*h^2-(x+b+1)^2)*2*(h+a1*s)+2*(s+a1*h)*(h^2+a1*s^2-(x+b+1)^2)+2*a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2)*t*dt+t^2*(a*(s^2+a1*h^2-(x+b+1)^2)*a*2*(h+a1*s)+a*2*(s+a1*h)*a*(h^2+a1*s^2-(x+b+1)^2))-t*((s^2+a1*h^2-(x+b+1)^2)*a*2*(h+s*a1)+2*(s+a1*h)*a*(h^2+a1*s^2-(x+b+1)^2)+a*(s^2+a1*h^2-(x+b+1)^2)*2*(h+a1*s)+a*2*(s+a1*h)*(h^2+a1*s^2-(x+b+1)^2))-2*a2*s*h(1-a*t)*(a2*(s+h)-a*a2*s*h*dt-a*a2*(s+h)*t)-dt*(a*(s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))));
dy(4)=du;
dy(5)=(1/((a*(s^2+a1*h^2-(x+b+1)^2)*t-(s^2+a1*h^2-(x+b+1)^2))))*((-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)+(a2*s*h-a*a2*s*h*t)*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du))));
dy(6) =(1/((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t))*((a2*s*h-(a*a2*s*h)*t)*((1/((((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t)*(((s^2+a1*h^2-(x+b+1).^2))-a*(s^2+a1*h^2-(x+b+1)*(x+b+1))*t))-(a2*s*h-(a*a2*s*h)*t)^2))*((a2*s*h-(a*a2*s*h)*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)-(((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t))*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*s*h*(a4+a1)*dt*du)))+(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE));
dy(7)=dt;
dy(8)=ddt;
dy(9)=(1/((a*(x+b+1)*(a5*(s^2+h^2)-a8*(x+b+1)*(x+b+1)))*t-((x+b+1)*(a5*s^2+a5*h^2-a8*(x+b+1)*(x+b+1)))))*((s^2+h^2+2*a5*s*+2*a5*h-a6*(x+b+1)*(x+b+1))*ddt+((2*a*a7*(x+b+1))*t-2*(x+b+1)*(a7-a*a11))*((1/((((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t)*(((s^2+a1*h^2-(x+b+1)*(x+b+1)))-a*(s^2+a1*h^2-(x+b+1)*(x+b+1))*t))-(a2*s*h-(a*a2*s*h)*t)^2))*((a2*s*h-(a*a2*s*h)*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)-(((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t))*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*s*h*(a4+a1)*dt*du)))+((a*2*a7)*t-(2*(x+b+1)*(a7-2*a*a11)))*((1/((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t))*((a2*s*h-(a*a2*s*h)*t)*((1/((((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t)*(((s^2+a1*h^2-(x+b+1)*(x+b+1)))-a*(s^2+a1*h^2-(x+b+1)*(x+b+1))*t))-(a2*s*h-(a*a2*s*h)*t)^2))*((a2*s*h-(a*a2*s*h)*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)-(((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t))*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*s*h*(a4+a1)*dt*du)))+(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)))-a*(s^2+h^2+2*a5*s+2*a5*h-a6*(x+b+1)*(x+b+1))*t*ddt-a*(s^2+h^2+a5*s+a5*h)*dt*dt-a*(x+b+1)*(a5*s^2+a5*h^2+a10*(x+b+1)*(x+b+1))*dt*ddt);
end
function res = projbc(ya,yb)
res = [ya(1);
ya(4);
ya(7)-1;
ya(3);
ya(5);
yb(1);
yb(4);
yb(7)-0.5;
yb(9)];
end
end pvb4c MATLAB Answers — New Questions
Simulation issues with current control with a 3 phase inverter
Im working on the following simulation.
Where im using the programmable voltage source as a representation of the grid and than im using a inductance and resistance with 3mH and 50 mOhm and than im using a Average value voltage source converter representing a bidirectional inverter and than a dc link with a batterie with 800V.
The following is my current control algorithm,
The control signal is than put into a PWM Timing and Waveform Generator to control the inverter.
The issue im currently facing is that i cant control the current for some reason the current id is not following the id* current, i tried tuning the PI controller but that doesnt help. I still get the following currents even tho they should go to 0 since id* and iq* are both 0.
I then tried to run the vd voltage as the vd inv voltage and the vq as the vq inv Voltage but there is still some residual current in the system even tho it should be 0 at that point.
I really tried a lot of different approaches like measuring the current between inductance and inverter, and also played with the sample time but i never get the current id and iq to follow id* and iq* i always get this current form and i dont really understand why.
Is my simulation wrong physically or am i not seeing something?
I also put a copy of my simulation below in case someone wants to test with it.
Any kind of help or new leads as why this current controller doesnt work would be much appreciated.Im working on the following simulation.
Where im using the programmable voltage source as a representation of the grid and than im using a inductance and resistance with 3mH and 50 mOhm and than im using a Average value voltage source converter representing a bidirectional inverter and than a dc link with a batterie with 800V.
The following is my current control algorithm,
The control signal is than put into a PWM Timing and Waveform Generator to control the inverter.
The issue im currently facing is that i cant control the current for some reason the current id is not following the id* current, i tried tuning the PI controller but that doesnt help. I still get the following currents even tho they should go to 0 since id* and iq* are both 0.
I then tried to run the vd voltage as the vd inv voltage and the vq as the vq inv Voltage but there is still some residual current in the system even tho it should be 0 at that point.
I really tried a lot of different approaches like measuring the current between inductance and inverter, and also played with the sample time but i never get the current id and iq to follow id* and iq* i always get this current form and i dont really understand why.
Is my simulation wrong physically or am i not seeing something?
I also put a copy of my simulation below in case someone wants to test with it.
Any kind of help or new leads as why this current controller doesnt work would be much appreciated. Im working on the following simulation.
Where im using the programmable voltage source as a representation of the grid and than im using a inductance and resistance with 3mH and 50 mOhm and than im using a Average value voltage source converter representing a bidirectional inverter and than a dc link with a batterie with 800V.
The following is my current control algorithm,
The control signal is than put into a PWM Timing and Waveform Generator to control the inverter.
The issue im currently facing is that i cant control the current for some reason the current id is not following the id* current, i tried tuning the PI controller but that doesnt help. I still get the following currents even tho they should go to 0 since id* and iq* are both 0.
I then tried to run the vd voltage as the vd inv voltage and the vq as the vq inv Voltage but there is still some residual current in the system even tho it should be 0 at that point.
I really tried a lot of different approaches like measuring the current between inductance and inverter, and also played with the sample time but i never get the current id and iq to follow id* and iq* i always get this current form and i dont really understand why.
Is my simulation wrong physically or am i not seeing something?
I also put a copy of my simulation below in case someone wants to test with it.
Any kind of help or new leads as why this current controller doesnt work would be much appreciated. current control, error, inverter control, bidirectional grid simulation, simulation MATLAB Answers — New Questions
Simulink pump transfer function output remains zero
Hello,
I am working on a pump station model in MATLAB/Simulink with a 110 kW induction motor and centrifugal pump.
I derived the transfer function of the pump, but my system output stays at zero during simulation.
Transfer function:
Gp(s) = …
Why does the output remain zero?
Is my model structure correct?
Thank you.Hello,
I am working on a pump station model in MATLAB/Simulink with a 110 kW induction motor and centrifugal pump.
I derived the transfer function of the pump, but my system output stays at zero during simulation.
Transfer function:
Gp(s) = …
Why does the output remain zero?
Is my model structure correct?
Thank you. Hello,
I am working on a pump station model in MATLAB/Simulink with a 110 kW induction motor and centrifugal pump.
I derived the transfer function of the pump, but my system output stays at zero during simulation.
Transfer function:
Gp(s) = …
Why does the output remain zero?
Is my model structure correct?
Thank you. simulink, matlab, transfer function, pump station, simulation, fuzzy logic controller MATLAB Answers — New Questions
Please help me to solve simple error in definition of dy(6)
proj()
function sol= proj
myLegend1 = {};
myLegend2 = {};
k0=386; ce=3.831*10^2;rho=89.54*10^2;alfat=1.78*10^-5;taw=0.5;Tnot=2.93*10^2;mu=38.6*10^6; lamda=77.6*10^6;
%lamda=77.6e^9;
%mu=38.6*e^9;lamda=77.6e+9
c0=sqrt((lamda+2*mu)/(rho)); Betanot=(3*lamda+2*mu)*alfat; a1=mu/(lamda+2*mu);a2=(mu+lamda)/(lamda+2*mu);a3=(Betanot*Tnot)/(lamda+2*mu);omega=(rho*ce)/(k0);
a4=lamda/(lamda+2*mu);a5=(k0*omega*c0^2)/(k0);a6=(rho*ce*c0^2)/(k0);
a7=(Betanot*c0^2)/(k0); a8=a6*taw; a9=a7*taw; a10=rho*ce*taw*omega*c0^4/(k0); a11=Betanot*taw*omega*c0^4/(k0);w=rho*ce/(k0);
rr = [0.1 0.3 0.5];
for i =1:numel(rr)
a= rr(i);
s=0.001;h=0.001;b=0.01;
y0 = [0,0,0,0,0,0,1,0,0];
disp(a7)
options =bvpset(‘stats’,’on’,’RelTol’,1e-4);
m = linspace(0,3);
solinit = bvpinit(m,y0);
sol= bvp4c(@projfun,@projbc,solinit,options);
figure(1)
plot(sol.x,abs(sol.y(4,:)))
grid on,hold on
myLegend1{i}=[‘alfa= ‘,num2str(rr(i))];
figure(2)
plot(sol.x,(sol.y(5,:)))
title(‘Temperature’)
grid on,hold on
myLegend2{i}=[‘alfa= ‘,num2str(rr(i))];
i=i+1;
end
figure(1)
legend(myLegend1)
hold on
figure(2)
legend(myLegend2)
function dy = projfun(x,y)
dy = zeros(9,1);
E = y(1);
dE = y(2);
ddE=y(3);
u = y(4);
du = y(5);
ddu=y(6);
t = y(7);
dt = y(8);
ddt=y(9);
dy(1) = dE;
dy(2)=(1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du));
dy(3)=((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2)^2))*((((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*(a2*s*h*(1-a*t)*(2*a*a3*s*(t*ddt+dt*dt)+2*a*a3*t*dt-a3*s*ddt-a3*dt-s*(s^2+a1*h^2)*(dt*((1/((a*(s^2+a1*h^2-(x+b+1)^2)*t-(s^2+a1*h^2-(x+b+1)^2))))*((-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)+(a2*s*h-a*a2*s*h*t)*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))))+ddt*du)-a*2*(s+a1*h)*dt*du-a*s*h*(a4+a1)*(dt*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))+dt*dE)-a*(a4*(s+h)+a1*(s+h))*dt*dE)+(a2*(s+h)-a*a2*s*h*dt-a*a2*(s+h)*t)*(2*a*a3*s*t*dt-a3*s*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)-((1-a*t)*(s^2+a1*h^2-(x+b+1)^2)*((2*a*a3*h)*(t*ddt+dt*dt)+2*a*a3*t*dt-dt*a3-ddt*a3*h-dt*du*a*(a4+a1)*(s+h)-a*(h^2+a1*s^2)*(dt*(((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))+ddt*dE))-dt*dE*a*2*(h+s)-(dt*((1/((a*(s^2+a1*h^2-(x+b+1)^2)*t-(s^2+a1*h^2-(x+b+1)^2))))*((-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)+(a2*s*h-a*a2*s*h*t)*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))))+dt*du)*a*s*h*(a4+a1))-(2*a*a3*s*t*dt-a3*s*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)*(2*(s+a1*h)-a*(s^2+a1*h^2-(x+1+b)^2)*dt-a*2*(s+a1*h)*t))-(a2*s*h*(1-a*t)*(2*a*a3*s*t*dt-a3*s*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)-(s^2+a1*h^2-(x+b+1)^2)*(1-a*t)*(2*a*a3*h*t*dt-a3*h*dt-a*(h^2+a1*s^2)*dt*dE-a*s*h*(a4+a1)*dt*du))*((s^2+a1*h^2-(x+b+1)^2)*2*(h+s)+2*(s+a1*h)*(h^2+a1*s^2-(x+b+1)^2)+2*a*(s^2+a1*h^2-(x+1+b)^2)*a*(h^2+a1*s^2-(x+b+1)^2)*t*dt)+t^2*(a*2*(s+h)*a*(h^2+a1*s^2-(x+1+b)^2)+a*(s^2+a1*h^2-(x+b+1)^2)*a*2*(h+a1*s))-(a*(s^2+a1*h^2-(x+1+b)^2)*(h^2+a1*s^2-(x+1+b)^2)+(s^2+a1*h^2-(x+1+b)^2)*a*(h^2+a1*s^2-(x+1+b)^2))*dt-t*(a*(s^2+a1*h^2-(x+1+b)^2)*2*(h+a1*s)+a*2*(s+a1*h)*(h^2+a1*s^2-(x+1+b)^2)+(s^2+a1*h^2-(x+1+b)^2)*a*(h^2+a1*s^2-(x+1+b)^2)+2*(s+a1*h)*a*(h^2+a1*s^2-(x+1+b)^2))-2*a2*s*h*(1-a*t)*(a2*(s+h)-a*a2*s*h*dt-a*s*2*(s+h)*t)));
dy(4)=du;
dy(5)=(1/((a*(s^2+a1*h^2-(x+b+1)^2)*t-(s^2+a1*h^2-(x+b+1)^2))))*((-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)+(a2*s*h-a*a2*s*h*t)*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du))));
dy(6) =(1/(-(s^2+a1*h^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2))*t)^2)*(-(((-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)+(a2*s*h-a*a2*s*h*t)*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))))*(a*((s^2+a1*h^2-(x+b+1)^2))*dt+a*2*(s+a1*h)*t-2*(s+a1*h))+(a*t-1)*(s^2+a1*h^2-(x+b+1)^2)*((a2*s*h-(a*a2*s*h)*t)*(((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2)^2))*((((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*(a2*s*h*(1-a*t)*(2*a*a3*s*(t*ddt+dt*dt)+2*a*a3*t*dt-a3*s*ddt-a3*dt-s*(s^2+a1*h^2)*(dt*((1/((a*(s^2+a1*h^2-(x+b+1)^2)*t-(s^2+a1*h^2-(x+b+1)^2))))*((-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)+(a2*s*h-a*a2*s*h*t)*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))))+ddt*du)-a*2*(s+a1*h)*dt*du-a*s*h*(a4+a1)*(dt*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))+dt*dE)-a*(a4*(s+h)+a1*(s+h))*dt*dE)+(a2*(s+h)-a*a2*s*h*dt-a*a2*(s+h)*t)*(2*a*a3*s*t*dt-a3*s*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)-((1-a*t)*(s^2+a1*h^2-(x+b+1)^2)*((2*a*a3*h)*(t*ddt+dt*dt)+2*a*a3*t*dt-dt*a3-ddt*a3*h-dt*du*a*(a4+a1)*(s+h)-a*(h^2+a1*s^2)*(dt*(((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))+ddt*dE))-dt*dE*a*2*(h+s)-(dt*((1/((a*(s^2+a1*h^2-(x+b+1)^2)*t-(s^2+a1*h^2-(x+b+1)^2))))*((-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)+(a2*s*h-a*a2*s*h*t)*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))))+dt*du)*a*s*h*(a4+a1))-(2*a*a3*s*t*dt-a3*s*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)*(2*(s+a1*h)-a*(s^2+a1*h^2-(x+1+b)^2)*dt-a*2*(s+a1*h)*t))-(a2*s*h*(1-a*t)*(2*a*a3*s*t*dt-a3*s*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)-(s^2+a1*h^2-(x+b+1)^2)*(1-a*t)*(2*a*a3*h*t*dt-a3*h*dt-a*(h^2+a1*s^2)*dt*dE-a*s*h*(a4+a1)*dt*du))*((s^2+a1*h^2-(x+b+1)^2)*2*(h+s)+2*(s+a1*h)*(h^2+a1*s^2-(x+b+1)^2)+2*a*(s^2+a1*h^2-(x+1+b)^2)*a*(h^2+a1*s^2-(x+b+1)^2)*t*dt)+t^2*(a*2*(s+h)*a*(h^2+a1*s^2-(x+1+b)^2)+a*(s^2+a1*h^2-(x+b+1)^2)*a*2*(h+a1*s))-(a*(s^2+a1*h^2-(x+1+b)^2)*(h^2+a1*s^2-(x+1+b)^2)+(s^2+a1*h^2-(x+1+b)^2)*a*(h^2+a1*s^2-(x+1+b)^2))*dt-t*(a*(s^2+a1*h^2-(x+1+b)^2)*2*(h+a1*s)+a*2*(s+a1*h)*(h^2+a1*s^2-(x+1+b)^2)+(s^2+a1*h^2-(x+1+b)^2)*a*(h^2+a1*s^2-(x+1+b)^2)+2*(s+a1*h)*a*(h^2+a1*s^2-(x+1+b)^2))-2*a2*s*h*(1-a*t)*(a2*(s+h)-a*a2*s*h*dt-a*s*2*(s+h)*t))))+(a2*(s+h)-a*a2*s*h*dt-a*a2*(s+h)*t)*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du))-a3*s*ddt-a3*dt+2*a*a3*s*(t*ddt+dt*dt)+2*a*a3*t*dt-a*2*(s+a1*h)*dt*du-a*(s^2+a1*h^2)*(dt*((1/((a*(s^2+a1*h^2-(x+b+1)^2)*t-(s^2+a1*h^2-(x+b+1)^2))))*((-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)+(a2*s*h-a*a2*s*h*t)*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))))+ddt*du))-a*(a4*(s+h)+a1*(s+h))*dt*dE-a*s*h*(a4+a1)*(dt*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))+ddt*dE)));
dy(7)=dt;
dy(8)=ddt;
dy(9)=(1/((a*(x+b+1)*(a5*(s^2+h^2)-a8*(x+b+1)*(x+b+1)))*t-((x+b+1)*(a5*s^2+a5*h^2-a8*(x+b+1)*(x+b+1)))))*((s^2+h^2+2*a5*s*+2*a5*h-a6*(x+b+1)*(x+b+1))*ddt+((2*a*a7*(x+b+1))*t-2*(x+b+1)*(a7-a*a11))*((1/((((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t)*(((s^2+a1*h^2-(x+b+1)*(x+b+1)))-a*(s^2+a1*h^2-(x+b+1)*(x+b+1))*t))-(a2*s*h-(a*a2*s*h)*t)^2))*((a2*s*h-(a*a2*s*h)*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)-(((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t))*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*s*h*(a4+a1)*dt*du)))+((a*2*a7)*t-(2*(x+b+1)*(a7-2*a*a11)))*((1/((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t))*((a2*s*h-(a*a2*s*h)*t)*((1/((((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t)*(((s^2+a1*h^2-(x+b+1)*(x+b+1)))-a*(s^2+a1*h^2-(x+b+1)*(x+b+1))*t))-(a2*s*h-(a*a2*s*h)*t)^2))*((a2*s*h-(a*a2*s*h)*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)-(((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t))*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*s*h*(a4+a1)*dt*du)))+(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)))-a*(s^2+h^2+2*a5*s+2*a5*h-a6*(x+b+1)*(x+b+1))*t*ddt-a*(s^2+h^2+a5*s+a5*h)*dt*dt-a*(x+b+1)*(a5*s^2+a5*h^2+a10*(x+b+1)*(x+b+1))*dt*ddt);
end
function res = projbc(ya,yb)
res = [ya(1);
ya(4);
ya(7)-1;
ya(3);
ya(6);
yb(1);
yb(4);
yb(7)-0.5;
yb(9)];
end
endproj()
function sol= proj
myLegend1 = {};
myLegend2 = {};
k0=386; ce=3.831*10^2;rho=89.54*10^2;alfat=1.78*10^-5;taw=0.5;Tnot=2.93*10^2;mu=38.6*10^6; lamda=77.6*10^6;
%lamda=77.6e^9;
%mu=38.6*e^9;lamda=77.6e+9
c0=sqrt((lamda+2*mu)/(rho)); Betanot=(3*lamda+2*mu)*alfat; a1=mu/(lamda+2*mu);a2=(mu+lamda)/(lamda+2*mu);a3=(Betanot*Tnot)/(lamda+2*mu);omega=(rho*ce)/(k0);
a4=lamda/(lamda+2*mu);a5=(k0*omega*c0^2)/(k0);a6=(rho*ce*c0^2)/(k0);
a7=(Betanot*c0^2)/(k0); a8=a6*taw; a9=a7*taw; a10=rho*ce*taw*omega*c0^4/(k0); a11=Betanot*taw*omega*c0^4/(k0);w=rho*ce/(k0);
rr = [0.1 0.3 0.5];
for i =1:numel(rr)
a= rr(i);
s=0.001;h=0.001;b=0.01;
y0 = [0,0,0,0,0,0,1,0,0];
disp(a7)
options =bvpset(‘stats’,’on’,’RelTol’,1e-4);
m = linspace(0,3);
solinit = bvpinit(m,y0);
sol= bvp4c(@projfun,@projbc,solinit,options);
figure(1)
plot(sol.x,abs(sol.y(4,:)))
grid on,hold on
myLegend1{i}=[‘alfa= ‘,num2str(rr(i))];
figure(2)
plot(sol.x,(sol.y(5,:)))
title(‘Temperature’)
grid on,hold on
myLegend2{i}=[‘alfa= ‘,num2str(rr(i))];
i=i+1;
end
figure(1)
legend(myLegend1)
hold on
figure(2)
legend(myLegend2)
function dy = projfun(x,y)
dy = zeros(9,1);
E = y(1);
dE = y(2);
ddE=y(3);
u = y(4);
du = y(5);
ddu=y(6);
t = y(7);
dt = y(8);
ddt=y(9);
dy(1) = dE;
dy(2)=(1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du));
dy(3)=((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2)^2))*((((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*(a2*s*h*(1-a*t)*(2*a*a3*s*(t*ddt+dt*dt)+2*a*a3*t*dt-a3*s*ddt-a3*dt-s*(s^2+a1*h^2)*(dt*((1/((a*(s^2+a1*h^2-(x+b+1)^2)*t-(s^2+a1*h^2-(x+b+1)^2))))*((-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)+(a2*s*h-a*a2*s*h*t)*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))))+ddt*du)-a*2*(s+a1*h)*dt*du-a*s*h*(a4+a1)*(dt*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))+dt*dE)-a*(a4*(s+h)+a1*(s+h))*dt*dE)+(a2*(s+h)-a*a2*s*h*dt-a*a2*(s+h)*t)*(2*a*a3*s*t*dt-a3*s*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)-((1-a*t)*(s^2+a1*h^2-(x+b+1)^2)*((2*a*a3*h)*(t*ddt+dt*dt)+2*a*a3*t*dt-dt*a3-ddt*a3*h-dt*du*a*(a4+a1)*(s+h)-a*(h^2+a1*s^2)*(dt*(((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))+ddt*dE))-dt*dE*a*2*(h+s)-(dt*((1/((a*(s^2+a1*h^2-(x+b+1)^2)*t-(s^2+a1*h^2-(x+b+1)^2))))*((-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)+(a2*s*h-a*a2*s*h*t)*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))))+dt*du)*a*s*h*(a4+a1))-(2*a*a3*s*t*dt-a3*s*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)*(2*(s+a1*h)-a*(s^2+a1*h^2-(x+1+b)^2)*dt-a*2*(s+a1*h)*t))-(a2*s*h*(1-a*t)*(2*a*a3*s*t*dt-a3*s*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)-(s^2+a1*h^2-(x+b+1)^2)*(1-a*t)*(2*a*a3*h*t*dt-a3*h*dt-a*(h^2+a1*s^2)*dt*dE-a*s*h*(a4+a1)*dt*du))*((s^2+a1*h^2-(x+b+1)^2)*2*(h+s)+2*(s+a1*h)*(h^2+a1*s^2-(x+b+1)^2)+2*a*(s^2+a1*h^2-(x+1+b)^2)*a*(h^2+a1*s^2-(x+b+1)^2)*t*dt)+t^2*(a*2*(s+h)*a*(h^2+a1*s^2-(x+1+b)^2)+a*(s^2+a1*h^2-(x+b+1)^2)*a*2*(h+a1*s))-(a*(s^2+a1*h^2-(x+1+b)^2)*(h^2+a1*s^2-(x+1+b)^2)+(s^2+a1*h^2-(x+1+b)^2)*a*(h^2+a1*s^2-(x+1+b)^2))*dt-t*(a*(s^2+a1*h^2-(x+1+b)^2)*2*(h+a1*s)+a*2*(s+a1*h)*(h^2+a1*s^2-(x+1+b)^2)+(s^2+a1*h^2-(x+1+b)^2)*a*(h^2+a1*s^2-(x+1+b)^2)+2*(s+a1*h)*a*(h^2+a1*s^2-(x+1+b)^2))-2*a2*s*h*(1-a*t)*(a2*(s+h)-a*a2*s*h*dt-a*s*2*(s+h)*t)));
dy(4)=du;
dy(5)=(1/((a*(s^2+a1*h^2-(x+b+1)^2)*t-(s^2+a1*h^2-(x+b+1)^2))))*((-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)+(a2*s*h-a*a2*s*h*t)*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du))));
dy(6) =(1/(-(s^2+a1*h^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2))*t)^2)*(-(((-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)+(a2*s*h-a*a2*s*h*t)*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))))*(a*((s^2+a1*h^2-(x+b+1)^2))*dt+a*2*(s+a1*h)*t-2*(s+a1*h))+(a*t-1)*(s^2+a1*h^2-(x+b+1)^2)*((a2*s*h-(a*a2*s*h)*t)*(((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2)^2))*((((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*(a2*s*h*(1-a*t)*(2*a*a3*s*(t*ddt+dt*dt)+2*a*a3*t*dt-a3*s*ddt-a3*dt-s*(s^2+a1*h^2)*(dt*((1/((a*(s^2+a1*h^2-(x+b+1)^2)*t-(s^2+a1*h^2-(x+b+1)^2))))*((-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)+(a2*s*h-a*a2*s*h*t)*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))))+ddt*du)-a*2*(s+a1*h)*dt*du-a*s*h*(a4+a1)*(dt*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))+dt*dE)-a*(a4*(s+h)+a1*(s+h))*dt*dE)+(a2*(s+h)-a*a2*s*h*dt-a*a2*(s+h)*t)*(2*a*a3*s*t*dt-a3*s*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)-((1-a*t)*(s^2+a1*h^2-(x+b+1)^2)*((2*a*a3*h)*(t*ddt+dt*dt)+2*a*a3*t*dt-dt*a3-ddt*a3*h-dt*du*a*(a4+a1)*(s+h)-a*(h^2+a1*s^2)*(dt*(((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))+ddt*dE))-dt*dE*a*2*(h+s)-(dt*((1/((a*(s^2+a1*h^2-(x+b+1)^2)*t-(s^2+a1*h^2-(x+b+1)^2))))*((-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)+(a2*s*h-a*a2*s*h*t)*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))))+dt*du)*a*s*h*(a4+a1))-(2*a*a3*s*t*dt-a3*s*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)*(2*(s+a1*h)-a*(s^2+a1*h^2-(x+1+b)^2)*dt-a*2*(s+a1*h)*t))-(a2*s*h*(1-a*t)*(2*a*a3*s*t*dt-a3*s*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)-(s^2+a1*h^2-(x+b+1)^2)*(1-a*t)*(2*a*a3*h*t*dt-a3*h*dt-a*(h^2+a1*s^2)*dt*dE-a*s*h*(a4+a1)*dt*du))*((s^2+a1*h^2-(x+b+1)^2)*2*(h+s)+2*(s+a1*h)*(h^2+a1*s^2-(x+b+1)^2)+2*a*(s^2+a1*h^2-(x+1+b)^2)*a*(h^2+a1*s^2-(x+b+1)^2)*t*dt)+t^2*(a*2*(s+h)*a*(h^2+a1*s^2-(x+1+b)^2)+a*(s^2+a1*h^2-(x+b+1)^2)*a*2*(h+a1*s))-(a*(s^2+a1*h^2-(x+1+b)^2)*(h^2+a1*s^2-(x+1+b)^2)+(s^2+a1*h^2-(x+1+b)^2)*a*(h^2+a1*s^2-(x+1+b)^2))*dt-t*(a*(s^2+a1*h^2-(x+1+b)^2)*2*(h+a1*s)+a*2*(s+a1*h)*(h^2+a1*s^2-(x+1+b)^2)+(s^2+a1*h^2-(x+1+b)^2)*a*(h^2+a1*s^2-(x+1+b)^2)+2*(s+a1*h)*a*(h^2+a1*s^2-(x+1+b)^2))-2*a2*s*h*(1-a*t)*(a2*(s+h)-a*a2*s*h*dt-a*s*2*(s+h)*t))))+(a2*(s+h)-a*a2*s*h*dt-a*a2*(s+h)*t)*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du))-a3*s*ddt-a3*dt+2*a*a3*s*(t*ddt+dt*dt)+2*a*a3*t*dt-a*2*(s+a1*h)*dt*du-a*(s^2+a1*h^2)*(dt*((1/((a*(s^2+a1*h^2-(x+b+1)^2)*t-(s^2+a1*h^2-(x+b+1)^2))))*((-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)+(a2*s*h-a*a2*s*h*t)*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))))+ddt*du))-a*(a4*(s+h)+a1*(s+h))*dt*dE-a*s*h*(a4+a1)*(dt*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))+ddt*dE)));
dy(7)=dt;
dy(8)=ddt;
dy(9)=(1/((a*(x+b+1)*(a5*(s^2+h^2)-a8*(x+b+1)*(x+b+1)))*t-((x+b+1)*(a5*s^2+a5*h^2-a8*(x+b+1)*(x+b+1)))))*((s^2+h^2+2*a5*s*+2*a5*h-a6*(x+b+1)*(x+b+1))*ddt+((2*a*a7*(x+b+1))*t-2*(x+b+1)*(a7-a*a11))*((1/((((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t)*(((s^2+a1*h^2-(x+b+1)*(x+b+1)))-a*(s^2+a1*h^2-(x+b+1)*(x+b+1))*t))-(a2*s*h-(a*a2*s*h)*t)^2))*((a2*s*h-(a*a2*s*h)*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)-(((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t))*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*s*h*(a4+a1)*dt*du)))+((a*2*a7)*t-(2*(x+b+1)*(a7-2*a*a11)))*((1/((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t))*((a2*s*h-(a*a2*s*h)*t)*((1/((((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t)*(((s^2+a1*h^2-(x+b+1)*(x+b+1)))-a*(s^2+a1*h^2-(x+b+1)*(x+b+1))*t))-(a2*s*h-(a*a2*s*h)*t)^2))*((a2*s*h-(a*a2*s*h)*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)-(((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t))*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*s*h*(a4+a1)*dt*du)))+(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)))-a*(s^2+h^2+2*a5*s+2*a5*h-a6*(x+b+1)*(x+b+1))*t*ddt-a*(s^2+h^2+a5*s+a5*h)*dt*dt-a*(x+b+1)*(a5*s^2+a5*h^2+a10*(x+b+1)*(x+b+1))*dt*ddt);
end
function res = projbc(ya,yb)
res = [ya(1);
ya(4);
ya(7)-1;
ya(3);
ya(6);
yb(1);
yb(4);
yb(7)-0.5;
yb(9)];
end
end proj()
function sol= proj
myLegend1 = {};
myLegend2 = {};
k0=386; ce=3.831*10^2;rho=89.54*10^2;alfat=1.78*10^-5;taw=0.5;Tnot=2.93*10^2;mu=38.6*10^6; lamda=77.6*10^6;
%lamda=77.6e^9;
%mu=38.6*e^9;lamda=77.6e+9
c0=sqrt((lamda+2*mu)/(rho)); Betanot=(3*lamda+2*mu)*alfat; a1=mu/(lamda+2*mu);a2=(mu+lamda)/(lamda+2*mu);a3=(Betanot*Tnot)/(lamda+2*mu);omega=(rho*ce)/(k0);
a4=lamda/(lamda+2*mu);a5=(k0*omega*c0^2)/(k0);a6=(rho*ce*c0^2)/(k0);
a7=(Betanot*c0^2)/(k0); a8=a6*taw; a9=a7*taw; a10=rho*ce*taw*omega*c0^4/(k0); a11=Betanot*taw*omega*c0^4/(k0);w=rho*ce/(k0);
rr = [0.1 0.3 0.5];
for i =1:numel(rr)
a= rr(i);
s=0.001;h=0.001;b=0.01;
y0 = [0,0,0,0,0,0,1,0,0];
disp(a7)
options =bvpset(‘stats’,’on’,’RelTol’,1e-4);
m = linspace(0,3);
solinit = bvpinit(m,y0);
sol= bvp4c(@projfun,@projbc,solinit,options);
figure(1)
plot(sol.x,abs(sol.y(4,:)))
grid on,hold on
myLegend1{i}=[‘alfa= ‘,num2str(rr(i))];
figure(2)
plot(sol.x,(sol.y(5,:)))
title(‘Temperature’)
grid on,hold on
myLegend2{i}=[‘alfa= ‘,num2str(rr(i))];
i=i+1;
end
figure(1)
legend(myLegend1)
hold on
figure(2)
legend(myLegend2)
function dy = projfun(x,y)
dy = zeros(9,1);
E = y(1);
dE = y(2);
ddE=y(3);
u = y(4);
du = y(5);
ddu=y(6);
t = y(7);
dt = y(8);
ddt=y(9);
dy(1) = dE;
dy(2)=(1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du));
dy(3)=((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2)^2))*((((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*(a2*s*h*(1-a*t)*(2*a*a3*s*(t*ddt+dt*dt)+2*a*a3*t*dt-a3*s*ddt-a3*dt-s*(s^2+a1*h^2)*(dt*((1/((a*(s^2+a1*h^2-(x+b+1)^2)*t-(s^2+a1*h^2-(x+b+1)^2))))*((-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)+(a2*s*h-a*a2*s*h*t)*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))))+ddt*du)-a*2*(s+a1*h)*dt*du-a*s*h*(a4+a1)*(dt*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))+dt*dE)-a*(a4*(s+h)+a1*(s+h))*dt*dE)+(a2*(s+h)-a*a2*s*h*dt-a*a2*(s+h)*t)*(2*a*a3*s*t*dt-a3*s*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)-((1-a*t)*(s^2+a1*h^2-(x+b+1)^2)*((2*a*a3*h)*(t*ddt+dt*dt)+2*a*a3*t*dt-dt*a3-ddt*a3*h-dt*du*a*(a4+a1)*(s+h)-a*(h^2+a1*s^2)*(dt*(((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))+ddt*dE))-dt*dE*a*2*(h+s)-(dt*((1/((a*(s^2+a1*h^2-(x+b+1)^2)*t-(s^2+a1*h^2-(x+b+1)^2))))*((-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)+(a2*s*h-a*a2*s*h*t)*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))))+dt*du)*a*s*h*(a4+a1))-(2*a*a3*s*t*dt-a3*s*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)*(2*(s+a1*h)-a*(s^2+a1*h^2-(x+1+b)^2)*dt-a*2*(s+a1*h)*t))-(a2*s*h*(1-a*t)*(2*a*a3*s*t*dt-a3*s*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)-(s^2+a1*h^2-(x+b+1)^2)*(1-a*t)*(2*a*a3*h*t*dt-a3*h*dt-a*(h^2+a1*s^2)*dt*dE-a*s*h*(a4+a1)*dt*du))*((s^2+a1*h^2-(x+b+1)^2)*2*(h+s)+2*(s+a1*h)*(h^2+a1*s^2-(x+b+1)^2)+2*a*(s^2+a1*h^2-(x+1+b)^2)*a*(h^2+a1*s^2-(x+b+1)^2)*t*dt)+t^2*(a*2*(s+h)*a*(h^2+a1*s^2-(x+1+b)^2)+a*(s^2+a1*h^2-(x+b+1)^2)*a*2*(h+a1*s))-(a*(s^2+a1*h^2-(x+1+b)^2)*(h^2+a1*s^2-(x+1+b)^2)+(s^2+a1*h^2-(x+1+b)^2)*a*(h^2+a1*s^2-(x+1+b)^2))*dt-t*(a*(s^2+a1*h^2-(x+1+b)^2)*2*(h+a1*s)+a*2*(s+a1*h)*(h^2+a1*s^2-(x+1+b)^2)+(s^2+a1*h^2-(x+1+b)^2)*a*(h^2+a1*s^2-(x+1+b)^2)+2*(s+a1*h)*a*(h^2+a1*s^2-(x+1+b)^2))-2*a2*s*h*(1-a*t)*(a2*(s+h)-a*a2*s*h*dt-a*s*2*(s+h)*t)));
dy(4)=du;
dy(5)=(1/((a*(s^2+a1*h^2-(x+b+1)^2)*t-(s^2+a1*h^2-(x+b+1)^2))))*((-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)+(a2*s*h-a*a2*s*h*t)*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du))));
dy(6) =(1/(-(s^2+a1*h^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2))*t)^2)*(-(((-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)+(a2*s*h-a*a2*s*h*t)*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))))*(a*((s^2+a1*h^2-(x+b+1)^2))*dt+a*2*(s+a1*h)*t-2*(s+a1*h))+(a*t-1)*(s^2+a1*h^2-(x+b+1)^2)*((a2*s*h-(a*a2*s*h)*t)*(((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2)^2))*((((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*(a2*s*h*(1-a*t)*(2*a*a3*s*(t*ddt+dt*dt)+2*a*a3*t*dt-a3*s*ddt-a3*dt-s*(s^2+a1*h^2)*(dt*((1/((a*(s^2+a1*h^2-(x+b+1)^2)*t-(s^2+a1*h^2-(x+b+1)^2))))*((-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)+(a2*s*h-a*a2*s*h*t)*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))))+ddt*du)-a*2*(s+a1*h)*dt*du-a*s*h*(a4+a1)*(dt*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))+dt*dE)-a*(a4*(s+h)+a1*(s+h))*dt*dE)+(a2*(s+h)-a*a2*s*h*dt-a*a2*(s+h)*t)*(2*a*a3*s*t*dt-a3*s*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)-((1-a*t)*(s^2+a1*h^2-(x+b+1)^2)*((2*a*a3*h)*(t*ddt+dt*dt)+2*a*a3*t*dt-dt*a3-ddt*a3*h-dt*du*a*(a4+a1)*(s+h)-a*(h^2+a1*s^2)*(dt*(((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))+ddt*dE))-dt*dE*a*2*(h+s)-(dt*((1/((a*(s^2+a1*h^2-(x+b+1)^2)*t-(s^2+a1*h^2-(x+b+1)^2))))*((-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)+(a2*s*h-a*a2*s*h*t)*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))))+dt*du)*a*s*h*(a4+a1))-(2*a*a3*s*t*dt-a3*s*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)*(2*(s+a1*h)-a*(s^2+a1*h^2-(x+1+b)^2)*dt-a*2*(s+a1*h)*t))-(a2*s*h*(1-a*t)*(2*a*a3*s*t*dt-a3*s*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)-(s^2+a1*h^2-(x+b+1)^2)*(1-a*t)*(2*a*a3*h*t*dt-a3*h*dt-a*(h^2+a1*s^2)*dt*dE-a*s*h*(a4+a1)*dt*du))*((s^2+a1*h^2-(x+b+1)^2)*2*(h+s)+2*(s+a1*h)*(h^2+a1*s^2-(x+b+1)^2)+2*a*(s^2+a1*h^2-(x+1+b)^2)*a*(h^2+a1*s^2-(x+b+1)^2)*t*dt)+t^2*(a*2*(s+h)*a*(h^2+a1*s^2-(x+1+b)^2)+a*(s^2+a1*h^2-(x+b+1)^2)*a*2*(h+a1*s))-(a*(s^2+a1*h^2-(x+1+b)^2)*(h^2+a1*s^2-(x+1+b)^2)+(s^2+a1*h^2-(x+1+b)^2)*a*(h^2+a1*s^2-(x+1+b)^2))*dt-t*(a*(s^2+a1*h^2-(x+1+b)^2)*2*(h+a1*s)+a*2*(s+a1*h)*(h^2+a1*s^2-(x+1+b)^2)+(s^2+a1*h^2-(x+1+b)^2)*a*(h^2+a1*s^2-(x+1+b)^2)+2*(s+a1*h)*a*(h^2+a1*s^2-(x+1+b)^2))-2*a2*s*h*(1-a*t)*(a2*(s+h)-a*a2*s*h*dt-a*s*2*(s+h)*t))))+(a2*(s+h)-a*a2*s*h*dt-a*a2*(s+h)*t)*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du))-a3*s*ddt-a3*dt+2*a*a3*s*(t*ddt+dt*dt)+2*a*a3*t*dt-a*2*(s+a1*h)*dt*du-a*(s^2+a1*h^2)*(dt*((1/((a*(s^2+a1*h^2-(x+b+1)^2)*t-(s^2+a1*h^2-(x+b+1)^2))))*((-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)+(a2*s*h-a*a2*s*h*t)*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))))+ddt*du))-a*(a4*(s+h)+a1*(s+h))*dt*dE-a*s*h*(a4+a1)*(dt*((1/((s^2+a1*h^2-(x+b+1)^2)*(h^2+a1*s^2-(x+b+1)^2)+(a*(s^2+a1*h^2-(x+b+1)^2)*a*(h^2+a1*s^2-(x+b+1)^2))*t^2-(a*(s^2+a1*h^2-(x+b+1)^2)*((s^2+a1*h^2-(x+b+1)^2))+(s^2+a1*h^2-(x+b+1)^2)*a*(s^2+a1*h^2-(x+b+1)^2))*t-(a2*s*h-a*a2*s*h*t)^2))*((a2*s*h-a*a2*s*h*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-(a*a4*s*h+a*a1*s*h)*dt*dE)-((s^2+a1*h^2-(x+b+1)^2)-a*((s^2+a1*h^2-(x+b+1)^2))*t)*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*(a4*s*h+a1*s*h)*dt*du)))+ddt*dE)));
dy(7)=dt;
dy(8)=ddt;
dy(9)=(1/((a*(x+b+1)*(a5*(s^2+h^2)-a8*(x+b+1)*(x+b+1)))*t-((x+b+1)*(a5*s^2+a5*h^2-a8*(x+b+1)*(x+b+1)))))*((s^2+h^2+2*a5*s*+2*a5*h-a6*(x+b+1)*(x+b+1))*ddt+((2*a*a7*(x+b+1))*t-2*(x+b+1)*(a7-a*a11))*((1/((((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t)*(((s^2+a1*h^2-(x+b+1)*(x+b+1)))-a*(s^2+a1*h^2-(x+b+1)*(x+b+1))*t))-(a2*s*h-(a*a2*s*h)*t)^2))*((a2*s*h-(a*a2*s*h)*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)-(((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t))*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*s*h*(a4+a1)*dt*du)))+((a*2*a7)*t-(2*(x+b+1)*(a7-2*a*a11)))*((1/((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t))*((a2*s*h-(a*a2*s*h)*t)*((1/((((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t)*(((s^2+a1*h^2-(x+b+1)*(x+b+1)))-a*(s^2+a1*h^2-(x+b+1)*(x+b+1))*t))-(a2*s*h-(a*a2*s*h)*t)^2))*((a2*s*h-(a*a2*s*h)*t)*(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)-(((s^2+a1*h^2-(x+b+1)*(x+b+1))-(a*(s^2+a1*h^2-(x+b+1)*(x+b+1)))*t))*(-a3*h*dt+2*a*a3*h*t*dt-a*(h^2+a1*s^2)*dt*dE-a*s*h*(a4+a1)*dt*du)))+(-a3*s*dt+2*a*a3*s*t*dt-a*(s^2+a1*h^2)*dt*du-a*s*h*(a4+a1)*dt*dE)))-a*(s^2+h^2+2*a5*s+2*a5*h-a6*(x+b+1)*(x+b+1))*t*ddt-a*(s^2+h^2+a5*s+a5*h)*dt*dt-a*(x+b+1)*(a5*s^2+a5*h^2+a10*(x+b+1)*(x+b+1))*dt*ddt);
end
function res = projbc(ya,yb)
res = [ya(1);
ya(4);
ya(7)-1;
ya(3);
ya(6);
yb(1);
yb(4);
yb(7)-0.5;
yb(9)];
end
end pbp4c MATLAB Answers — New Questions
Planner’s Newly Redesigned Interface
Making Planner Look Nice Again
On February 23, 2026, Microsoft announced a refreshed design for the Planner user interface. In truth, I haven’t spent too much time thinking about the Planner interface since Microsoft launched the grid view in 2023. The interface was like an old sweater: comfortable for those who knew it with a couple of holes to avoid. Instead, any time I spent on Planner was occupied figuring out the details of the Planner Graph API to fill gaps left in the product, like analyzing unfinished tasks.
In any case, Microsoft is deploying the new UX across Microsoft 365. The deployment will take a few more weeks to reach all tenants, so be patient if you don’t see “enhanced navigation, responsive layouts, a new goals view for setting objectives and priorities, and task chat” turn up soon. Figure 1 shows tasks in a Planner plan presented in the board view. It all seems very much like the To Do UX.

Planner Task Chat
The feature that took my attention is Planner Task Chat. This is very different to the old comments functionality where users could leave notes about their views about a task and its attachments, checklist, and so on. Task Chat is a threaded conversation similar to what you see when people add comments to Office documents (Figure 2). A rudimentary rich-text editor (complete with emojis) is enough to get a point across.

Plan members who are @ mentioned receive notifications in the Teams activity feed and via email. Selecting a notification from the activity feed or email opens the task card (Figure 3), and the user can interact with the task from there. However, they don’t seem to be able to continue with the conversation. When I attempted to respond, Planner created three buckets called “What”, “How”, and “Step” to match some of the words I tried to input. I’m sure this is a bug that afflicts the task card in Teams. The same issue doesn’t occur when chatting through the Planner user interface.
Unlike comments, which Planner copied to everyone in the plan, task chat notifications only go to those who are mentioned.

Investigating APIs for Task Chat
A Graph API is supported for the older comment-style conversations (threads). However, no Graph API is currently available for the new task chats. In the past, Planner has taken time to support Graph APIs, so we might not see an API soon.
The same is true for Copilot chats. This information can be accessed (in a way) through the compliance records captured for Copilot or the aIInteractionHistory API, but it’s not as easy as navigating something like the comments for tasks. In any case, we’ll wait and see what transpires.
Planner Tasks and Goals
If you refer back to Figure 2, you’ll see the option to connect a task to a goal. Microsoft introduced goals for Planner about a year ago, but until now Goals have been a feature of Planner premium plans (aka Project). In their announcement, Microsoft says that basic Planner plans now include “a dedicated Goals view.” However, you’ll only see the options to connect tasks to goals and expose the goals view if you have a Microsoft 365 Copilot license or a Planner premium license.
Microsoft says that goals allow “teams to set clear, well-defined objectives to help prioritize work. By connecting tasks to shared goals, teams achieve greater alignment, gain clarity on priorities, and track progress and outcomes.” I guess that including goals for basic plans is a nice extra feature for those with Copilot licenses, but whether it’s worth an extra $10 month to upgrade to a Planner Plan 1 license is debatable. Choices!
Keep up to date with developments in apps like Planner by subscribing to the Office 365 for IT Pros eBook. Our monthly updates make sure that our subscribers understand the most important changes happening across Office 365.
Error using filterDesigner (line 85) Value must be a handle. macOS R2025b
>> filterDesigner
Error using filterDesigner (line 85)
Value must be a handle.
—-
>> ver
—————————————————————————————–
MATLAB Version: 25.2.0.2998904 (R2025b)
MATLAB License Number: STUDENT
Operating System: macOS Version: 26.0.1 Build: 25A362
Java Version: Java 11.0.25+9-LTS with Amazon.com Inc. OpenJDK 64-Bit Server VM mixed mode
—————————————————————————————–
MATLAB Version 25.2 (R2025b)
Simulink Version 25.2 (R2025b)
Control System Toolbox Version 25.2 (R2025b)
Curve Fitting Toolbox Version 25.2 (R2025b)
DSP System Toolbox Version 25.2 (R2025b)
Global Optimization Toolbox Version 25.2 (R2025b)
Image Processing Toolbox Version 25.2 (R2025b)
Instrument Control Toolbox Version 25.2 (R2025b)
Optimization Toolbox Version 25.2 (R2025b)
Parallel Computing Toolbox Version 25.2 (R2025b)
Signal Processing Toolbox Version 25.2 (R2025b)
Simulink Control Design Version 25.2 (R2025b)
Simulink Design Optimization Version 25.2 (R2025b)
Statistics and Machine Learning Toolbox Version 25.2 (R2025b)
Symbolic Math Toolbox Version 25.2 (R2025b)
—
>> which filterDesigner -all
/Applications/MATLAB_R2025b.app/toolbox/signal/sigtools/filterDesigner.m
—
>> status = license(‘test’, ‘Signal_Toolbox’)
status =
1
—
These were the tests performed and checks, in addition:
reinstall the Signal Processing Toolbox and the DSP System Toolbox – Don’t work
I did a clean install of the complete Matlab
Even after all these tests and procedures I still get the error:
>> filterDesigner
Error using filterDesigner (line 85)
Value must be a handle.
How do I solve this problem??>> filterDesigner
Error using filterDesigner (line 85)
Value must be a handle.
—-
>> ver
—————————————————————————————–
MATLAB Version: 25.2.0.2998904 (R2025b)
MATLAB License Number: STUDENT
Operating System: macOS Version: 26.0.1 Build: 25A362
Java Version: Java 11.0.25+9-LTS with Amazon.com Inc. OpenJDK 64-Bit Server VM mixed mode
—————————————————————————————–
MATLAB Version 25.2 (R2025b)
Simulink Version 25.2 (R2025b)
Control System Toolbox Version 25.2 (R2025b)
Curve Fitting Toolbox Version 25.2 (R2025b)
DSP System Toolbox Version 25.2 (R2025b)
Global Optimization Toolbox Version 25.2 (R2025b)
Image Processing Toolbox Version 25.2 (R2025b)
Instrument Control Toolbox Version 25.2 (R2025b)
Optimization Toolbox Version 25.2 (R2025b)
Parallel Computing Toolbox Version 25.2 (R2025b)
Signal Processing Toolbox Version 25.2 (R2025b)
Simulink Control Design Version 25.2 (R2025b)
Simulink Design Optimization Version 25.2 (R2025b)
Statistics and Machine Learning Toolbox Version 25.2 (R2025b)
Symbolic Math Toolbox Version 25.2 (R2025b)
—
>> which filterDesigner -all
/Applications/MATLAB_R2025b.app/toolbox/signal/sigtools/filterDesigner.m
—
>> status = license(‘test’, ‘Signal_Toolbox’)
status =
1
—
These were the tests performed and checks, in addition:
reinstall the Signal Processing Toolbox and the DSP System Toolbox – Don’t work
I did a clean install of the complete Matlab
Even after all these tests and procedures I still get the error:
>> filterDesigner
Error using filterDesigner (line 85)
Value must be a handle.
How do I solve this problem?? >> filterDesigner
Error using filterDesigner (line 85)
Value must be a handle.
—-
>> ver
—————————————————————————————–
MATLAB Version: 25.2.0.2998904 (R2025b)
MATLAB License Number: STUDENT
Operating System: macOS Version: 26.0.1 Build: 25A362
Java Version: Java 11.0.25+9-LTS with Amazon.com Inc. OpenJDK 64-Bit Server VM mixed mode
—————————————————————————————–
MATLAB Version 25.2 (R2025b)
Simulink Version 25.2 (R2025b)
Control System Toolbox Version 25.2 (R2025b)
Curve Fitting Toolbox Version 25.2 (R2025b)
DSP System Toolbox Version 25.2 (R2025b)
Global Optimization Toolbox Version 25.2 (R2025b)
Image Processing Toolbox Version 25.2 (R2025b)
Instrument Control Toolbox Version 25.2 (R2025b)
Optimization Toolbox Version 25.2 (R2025b)
Parallel Computing Toolbox Version 25.2 (R2025b)
Signal Processing Toolbox Version 25.2 (R2025b)
Simulink Control Design Version 25.2 (R2025b)
Simulink Design Optimization Version 25.2 (R2025b)
Statistics and Machine Learning Toolbox Version 25.2 (R2025b)
Symbolic Math Toolbox Version 25.2 (R2025b)
—
>> which filterDesigner -all
/Applications/MATLAB_R2025b.app/toolbox/signal/sigtools/filterDesigner.m
—
>> status = license(‘test’, ‘Signal_Toolbox’)
status =
1
—
These were the tests performed and checks, in addition:
reinstall the Signal Processing Toolbox and the DSP System Toolbox – Don’t work
I did a clean install of the complete Matlab
Even after all these tests and procedures I still get the error:
>> filterDesigner
Error using filterDesigner (line 85)
Value must be a handle.
How do I solve this problem?? signal processing, filter, error, r2025b, macos MATLAB Answers — New Questions
Unable to find explicit solution on vector equation with solve
Hello !
I’m trying to solve static mechanics equations, hence implying vectors.
I tried with a simple case but Matlab is unable to find an explicit solution, though it should be solvable. It seems to me as if there is an error in the code preventing Matlab to properly spot the unknowns (which are vector components).
Here’s a minimal code example, with a couple of tries with solve :
syms g mS fS real positive
syms vR_S_1 vR_S_2 vR_S_3 real
vP_S = [0; 0; -mS * g];
vR_S = [vR_S_1; vR_S_2; vR_S_3];
S1 = solve([vP_S + vR_S == zeros(3, 1); vR_S(2)^2 == vR_S(3)^2 * fS^2 – vR_S(1)^2]’, [vR_S(3), vR_S(1)])
S2 = solve([vP_S + vR_S == zeros(3, 1); vR_S_2^2 == vR_S_3^2 * fS^2 – vR_S_1^2]’, [vR_S_3, vR_S_1])
S3 = solve(subs([vP_S + vR_S == zeros(3, 1); vR_S_2^2 == vR_S_3^2 * fS^2 – vR_S_1^2])’, [vR_S_3, vR_S_1])
Any clue about what’s going on ?
Many thanks in advance !Hello !
I’m trying to solve static mechanics equations, hence implying vectors.
I tried with a simple case but Matlab is unable to find an explicit solution, though it should be solvable. It seems to me as if there is an error in the code preventing Matlab to properly spot the unknowns (which are vector components).
Here’s a minimal code example, with a couple of tries with solve :
syms g mS fS real positive
syms vR_S_1 vR_S_2 vR_S_3 real
vP_S = [0; 0; -mS * g];
vR_S = [vR_S_1; vR_S_2; vR_S_3];
S1 = solve([vP_S + vR_S == zeros(3, 1); vR_S(2)^2 == vR_S(3)^2 * fS^2 – vR_S(1)^2]’, [vR_S(3), vR_S(1)])
S2 = solve([vP_S + vR_S == zeros(3, 1); vR_S_2^2 == vR_S_3^2 * fS^2 – vR_S_1^2]’, [vR_S_3, vR_S_1])
S3 = solve(subs([vP_S + vR_S == zeros(3, 1); vR_S_2^2 == vR_S_3^2 * fS^2 – vR_S_1^2])’, [vR_S_3, vR_S_1])
Any clue about what’s going on ?
Many thanks in advance ! Hello !
I’m trying to solve static mechanics equations, hence implying vectors.
I tried with a simple case but Matlab is unable to find an explicit solution, though it should be solvable. It seems to me as if there is an error in the code preventing Matlab to properly spot the unknowns (which are vector components).
Here’s a minimal code example, with a couple of tries with solve :
syms g mS fS real positive
syms vR_S_1 vR_S_2 vR_S_3 real
vP_S = [0; 0; -mS * g];
vR_S = [vR_S_1; vR_S_2; vR_S_3];
S1 = solve([vP_S + vR_S == zeros(3, 1); vR_S(2)^2 == vR_S(3)^2 * fS^2 – vR_S(1)^2]’, [vR_S(3), vR_S(1)])
S2 = solve([vP_S + vR_S == zeros(3, 1); vR_S_2^2 == vR_S_3^2 * fS^2 – vR_S_1^2]’, [vR_S_3, vR_S_1])
S3 = solve(subs([vP_S + vR_S == zeros(3, 1); vR_S_2^2 == vR_S_3^2 * fS^2 – vR_S_1^2])’, [vR_S_3, vR_S_1])
Any clue about what’s going on ?
Many thanks in advance ! solve, vectors, symbolic MATLAB Answers — New Questions
ldf or dbc convert to excel
are there some m script, that can convert ldf to excel, or dbc to excel?
as currently i learn and know about lin or can bus.are there some m script, that can convert ldf to excel, or dbc to excel?
as currently i learn and know about lin or can bus. are there some m script, that can convert ldf to excel, or dbc to excel?
as currently i learn and know about lin or can bus. lfd, dbc, excel MATLAB Answers — New Questions
unreachable and dead code
why i am getting unreachable and dead code warning , i am not able to understant.
if anyone knows, please help me.why i am getting unreachable and dead code warning , i am not able to understant.
if anyone knows, please help me. why i am getting unreachable and dead code warning , i am not able to understant.
if anyone knows, please help me. stateflow, dead code MATLAB Answers — New Questions
Extending Protection for Confidential SharePoint Online Files
Configure Document Libraries with Default Sensitivity Label for Downloaded Files
I think most people will agree that it’s good to protect confidential information. In a Microsoft 365 context, protection through the Azure rights-management encryption service is available through sensitivity labels, which can be applied manually (with E3 licenses) or automatically (with E5). Automatic application includes configuring document libraries with a default sensitivity label. When a document library has a default sensitivity label, SharePoint Online applies the label to new and modified Office and PDF files (if unlabeled). It’s a great way to make sure that items stored in document libraries receive protection with minimal impact on users.
Extending the concept to ensure that Office documents downloaded from libraries receive protection is a logical next step. The feature is relatively new, but the announcement in message center notification MC1208688 (29 December 2025, Microsoft 365 roadmap item 468888) that the Office Online applications will support sensitivity labels with user-defined permissions (UDP) caused me to take another look. Extending protection for downloaded files depends on sensitivity labels with UDP, hence the connection.
Preparing SharePoint Online
Sensitivity labels can protect files with preconfigured administrator-defined permissions or with UDP. The big difference is that file owners can configure UDP on a per-file basis. SharePoint Online has supported labels with administrator-defined permissions for years, but only added support for UDP labels in March 2025. This was an important step forward because it unlocked support for files protected by UDP labels in Purview solutions like DLP and eDiscovery.
To enable SharePoint Online to extend protection for downloaded Office files, an administrator must update tenant settings by running the Set-SPOTenant cmdlet. Make sure that you use the most recent version of the SharePoint Online management PowerShell module and run the command as follows.
Set-SPOTenant -ExtendPermissionsToUnprotectedFiles $true Confirm This cmdlet requires a premium license to access its full functionality. To learn more about the licensing requirements, as well as the general capabilities and limitations associated with this feature, please refer to the detailed documentation available at: https://aka.ms/ExtendSharePointPermission. [Y] Yes [N] No [?] Help (default is "Y"): y
The warning about the premium license refers to SharePoint Advanced Management,
Wait a couple of hours to allow the update to become effective across the tenant. You should then be able to update library settings to extend protection for downloaded files. The most important point here is that the default sensitivity label for the library must be a UDP label (Figure 1). Using a UDP label allows SharePoint Online to dynamically configure the permissions assigned for the label as it downloads the file from the library.

You cannot configure a document library to have a default sensitivity label for files added or modified in the library with a different label to protect downloaded files.
Effect on Files in the Document Library
After selecting a default sensitivity label and choosing to extend protection for downloaded files, SharePoint Online scans the document library and applies the selected label to all unlabeled Office and PDF files. It also finds labeled files without encryption and replaces the existing label with the default label. In other words, all Office and PDF files in the document library are now protected.
If you decide not to extend protection to downloaded files and revert to the original document library configuration, SharePoint Online restores files to their original state by either updating (to the prior label) or removing sensitivity labels from files.
Usage Rights
When a file is downloaded, SharePoint Online checks the access the user has to the file and translates that access to UDP usage rights (see this table mapping permissions to usage rights). SharePoint Online then applies a sensitivity label with the appropriate usage rights to the file before it is downloaded. The labeling process also happens for local copies of files synchronized by the OneDrive client. Following the download, the usage rights set in the UDP label allows the user to open the file (Figure 2).

Many document libraries belong to sites associated with Microsoft 365 groups (teams). In these cases, the user is either a group owner or group member and will have owner or edit permission.
The Link to the Mother Ship
The real magic in this solution is that the permissions assigned to downloaded files only work when online access is available to SharePoint. Microsoft calls this a “just in time layer of protection.”
Offline access to labeled files isn’t supported because SharePoint needs to be able to validate that the user continues to have the right to access the file. For example, if the user’s level of permission to the content changes, SharePoint must be able to make that adjustment for the downloaded file. In addition, if the user is removed as a site (group) member, or the file is deleted from the site or moves to another site, or the site is deleted, SharePoint nullifies access, and the user can no longer open the file.
Interestingly, if a file is subject to a hold and is deleted, it is still present in the preservation hold library and access is maintained. Although labeled files cannot be copied or moved to a different site, they can be moved to a different document library within the site.
A New Possibility
Extending protection to downloaded files is an option that deserves consideration if you want to make sure that confidential material doesn’t leak. If the concern is to stop people from downloading files, SharePoint has a block download policy that can be applied to sites to force users to work with files online. The block download policy is licensed through SharePoint advanced management. Corporate culture and user work habits are just two of the factors that will drive the decision about which approach to take. It’s nice to have choice!
Insight like this doesn’t come easily. You’ve got to know the technology and understand how to look behind the scenes. Benefit from the knowledge and experience of the Office 365 for IT Pros team by subscribing to the best eBook covering Office 365 and the wider Microsoft 365 ecosystem.
Create Timeseries Objekt in MATLAB with the property “StoredUnits”
I have various measured values in MATLAB and would like to convert them into a ‘timeseries’ object so that I can analyze them in SDI. To do this, however, the “StoredUnits” property of the ‘timeseries’ object must also be set so that the scaling for the data cursor can then be changed in SDI from, for example, “m/s” to “km/h.”
But “StoredUnits” is not offered in the properties of the ‘timeseries’ object.
% create timeseries-Objekt (example)
temp = timeseries(data, time, "Name", "test", "StoredUnits", "m/s")
Error:
Error using timeseries/init (line 153)
Invalid property name
The alternative method of loading the corresponding signal from the SDI into MATLAB and then setting the property results in the following message::
% get current run from SDI
countRun = Simulink.sdi.Run.getLatest;
% load respective signal
inSigID = getSignalByIndex(countRun, 1);
% set property
inSigID.StoredUnits = "m/s";
Error:
Unable to set the ‘StoredUnits’ property of class ‘Signal’ because it is read-only.
This raises the question: how can a ‘timeseries’ object with the “StoredUnits” property be created in MATLAB?I have various measured values in MATLAB and would like to convert them into a ‘timeseries’ object so that I can analyze them in SDI. To do this, however, the “StoredUnits” property of the ‘timeseries’ object must also be set so that the scaling for the data cursor can then be changed in SDI from, for example, “m/s” to “km/h.”
But “StoredUnits” is not offered in the properties of the ‘timeseries’ object.
% create timeseries-Objekt (example)
temp = timeseries(data, time, "Name", "test", "StoredUnits", "m/s")
Error:
Error using timeseries/init (line 153)
Invalid property name
The alternative method of loading the corresponding signal from the SDI into MATLAB and then setting the property results in the following message::
% get current run from SDI
countRun = Simulink.sdi.Run.getLatest;
% load respective signal
inSigID = getSignalByIndex(countRun, 1);
% set property
inSigID.StoredUnits = "m/s";
Error:
Unable to set the ‘StoredUnits’ property of class ‘Signal’ because it is read-only.
This raises the question: how can a ‘timeseries’ object with the “StoredUnits” property be created in MATLAB? I have various measured values in MATLAB and would like to convert them into a ‘timeseries’ object so that I can analyze them in SDI. To do this, however, the “StoredUnits” property of the ‘timeseries’ object must also be set so that the scaling for the data cursor can then be changed in SDI from, for example, “m/s” to “km/h.”
But “StoredUnits” is not offered in the properties of the ‘timeseries’ object.
% create timeseries-Objekt (example)
temp = timeseries(data, time, "Name", "test", "StoredUnits", "m/s")
Error:
Error using timeseries/init (line 153)
Invalid property name
The alternative method of loading the corresponding signal from the SDI into MATLAB and then setting the property results in the following message::
% get current run from SDI
countRun = Simulink.sdi.Run.getLatest;
% load respective signal
inSigID = getSignalByIndex(countRun, 1);
% set property
inSigID.StoredUnits = "m/s";
Error:
Unable to set the ‘StoredUnits’ property of class ‘Signal’ because it is read-only.
This raises the question: how can a ‘timeseries’ object with the “StoredUnits” property be created in MATLAB? sdi timeseries storedunits MATLAB Answers — New Questions
Resetting a memoized function
I know that clearCache will clear the cache of a MemoizedFunction, but how would you reset its other properties to their defaults? I would have thought that rebuilding it with memoize() would do so, but the test below shows that that does not work.
mf=memoize(@localFcn) %default property values
mf.CacheSize=3; mf.Enabled=false %make some non-default property settings
clear mf
mf=memoize(@localFcn) %clear and rebuild — but property values do not reset!!!!
function y=localFcn(x)
y=x.^2;
endI know that clearCache will clear the cache of a MemoizedFunction, but how would you reset its other properties to their defaults? I would have thought that rebuilding it with memoize() would do so, but the test below shows that that does not work.
mf=memoize(@localFcn) %default property values
mf.CacheSize=3; mf.Enabled=false %make some non-default property settings
clear mf
mf=memoize(@localFcn) %clear and rebuild — but property values do not reset!!!!
function y=localFcn(x)
y=x.^2;
end I know that clearCache will clear the cache of a MemoizedFunction, but how would you reset its other properties to their defaults? I would have thought that rebuilding it with memoize() would do so, but the test below shows that that does not work.
mf=memoize(@localFcn) %default property values
mf.CacheSize=3; mf.Enabled=false %make some non-default property settings
clear mf
mf=memoize(@localFcn) %clear and rebuild — but property values do not reset!!!!
function y=localFcn(x)
y=x.^2;
end memoize MATLAB Answers — New Questions
Can I configure a mex compiler on toolbox installation?
I have set of XML mexopts files and helper files that enable the use of the MinGW and Cygwin Fortran compilers on Windows on pre-R2024a releases. I’d like to package these in a toolbox like the compiler support package from Mathworks: https://www.mathworks.com/matlabcentral/fileexchange/52848-matlab-support-for-mingw-w64-c-c-fortran-compiler
On a fresh install of Matlab (i.e. mex not previously set up), installing that toolbox sets up the MinGW compilers. I don’t see a mechanism in the toolbox packaging tool to do this, though, and the only other answers I could find on this question suggest either having a check run the first time the user executes a toolbox function or having the user run a setup function.
Is there a way to do this automatically for user-created toolboxes?I have set of XML mexopts files and helper files that enable the use of the MinGW and Cygwin Fortran compilers on Windows on pre-R2024a releases. I’d like to package these in a toolbox like the compiler support package from Mathworks: https://www.mathworks.com/matlabcentral/fileexchange/52848-matlab-support-for-mingw-w64-c-c-fortran-compiler
On a fresh install of Matlab (i.e. mex not previously set up), installing that toolbox sets up the MinGW compilers. I don’t see a mechanism in the toolbox packaging tool to do this, though, and the only other answers I could find on this question suggest either having a check run the first time the user executes a toolbox function or having the user run a setup function.
Is there a way to do this automatically for user-created toolboxes? I have set of XML mexopts files and helper files that enable the use of the MinGW and Cygwin Fortran compilers on Windows on pre-R2024a releases. I’d like to package these in a toolbox like the compiler support package from Mathworks: https://www.mathworks.com/matlabcentral/fileexchange/52848-matlab-support-for-mingw-w64-c-c-fortran-compiler
On a fresh install of Matlab (i.e. mex not previously set up), installing that toolbox sets up the MinGW compilers. I don’t see a mechanism in the toolbox packaging tool to do this, though, and the only other answers I could find on this question suggest either having a check run the first time the user executes a toolbox function or having the user run a setup function.
Is there a way to do this automatically for user-created toolboxes? toolbox, mex MATLAB Answers — New Questions
I need my code to work/dont know what is going wrong.
I am working on a MATLAB assignment where I need to create a custom function called r_wheel.
The function should:
Take two inputs: bet_color and bet_amount
Return three outputs:
result_message (string saying if the bettor won or lost)
winner (0 if lost, 1 if won)
wager_message (string saying how much money was won or lost)
The payout rules are:
Red/Black → 1:1 payout
Green → 17:1 payout
If the bettor loses, they lose the amount wagered.
After that, I need to write a script that runs the function 100 times betting on "red" and calculates the odds of winning.
My issue is that I am not understanding how to get the function to be repeated multiple times and also add to a separate counter.
The error message I get is (Index exceeds the number of array elements. Index must not exceed 1.) Also, the code does not add to a counter, it instead only displays the answer one time.
This is the code for the function I made
function [result_msg,winner,wager_message] = r_wheel(bet_color, bet_amount)
disp(‘Spinning…’)
pause(2) %delay for suspense
random_int=randi([1 38]); %random # between 1 and 38
if random_int < 3 % if the # is less 1 or 2 then result is green
result_color = ‘Green’
wager_message = bet_amount*17 + bet_amount;
elseif (random_int <21) && (random_int>2)
result_color = ‘Red’ % if # is between 3 and 20 result is red
wager_message = bet_amount*2;
else
result_color = ‘Black’ %if # is between 21 and 38 the result is black
wager_message = bet_amount*2;
end
disp(result_color)
if strcmp(result_color, bet_color) % using string compare function to chekc if strings are the same
result_msg = ‘Congratulations! You win!’; % if bet color is correct set result to win
winner = 1; %set winner variable to 1
wager_message = wager_message
else
result_msg = ‘Sorry, you lose. Better luck next time!’; %if the bet color is not the same as result color set message
winner = 0; %set winner variable to 0
wager_message = -bet_amount
end
end
And here is the code for the loop.
clc, clear
x=’Red’
y= 15
win_count = 0
for i = 1:100
[result,winner]=r_wheel(x, y) % runs the function
win_count = 0
[result,winner]=r_wheel(x, y)
if winner(i)==1
win_count(i) = win_count(i)+1
else
win_count(i)= win_count(i)
end
end
disp(win_count)
disp(result)I am working on a MATLAB assignment where I need to create a custom function called r_wheel.
The function should:
Take two inputs: bet_color and bet_amount
Return three outputs:
result_message (string saying if the bettor won or lost)
winner (0 if lost, 1 if won)
wager_message (string saying how much money was won or lost)
The payout rules are:
Red/Black → 1:1 payout
Green → 17:1 payout
If the bettor loses, they lose the amount wagered.
After that, I need to write a script that runs the function 100 times betting on "red" and calculates the odds of winning.
My issue is that I am not understanding how to get the function to be repeated multiple times and also add to a separate counter.
The error message I get is (Index exceeds the number of array elements. Index must not exceed 1.) Also, the code does not add to a counter, it instead only displays the answer one time.
This is the code for the function I made
function [result_msg,winner,wager_message] = r_wheel(bet_color, bet_amount)
disp(‘Spinning…’)
pause(2) %delay for suspense
random_int=randi([1 38]); %random # between 1 and 38
if random_int < 3 % if the # is less 1 or 2 then result is green
result_color = ‘Green’
wager_message = bet_amount*17 + bet_amount;
elseif (random_int <21) && (random_int>2)
result_color = ‘Red’ % if # is between 3 and 20 result is red
wager_message = bet_amount*2;
else
result_color = ‘Black’ %if # is between 21 and 38 the result is black
wager_message = bet_amount*2;
end
disp(result_color)
if strcmp(result_color, bet_color) % using string compare function to chekc if strings are the same
result_msg = ‘Congratulations! You win!’; % if bet color is correct set result to win
winner = 1; %set winner variable to 1
wager_message = wager_message
else
result_msg = ‘Sorry, you lose. Better luck next time!’; %if the bet color is not the same as result color set message
winner = 0; %set winner variable to 0
wager_message = -bet_amount
end
end
And here is the code for the loop.
clc, clear
x=’Red’
y= 15
win_count = 0
for i = 1:100
[result,winner]=r_wheel(x, y) % runs the function
win_count = 0
[result,winner]=r_wheel(x, y)
if winner(i)==1
win_count(i) = win_count(i)+1
else
win_count(i)= win_count(i)
end
end
disp(win_count)
disp(result) I am working on a MATLAB assignment where I need to create a custom function called r_wheel.
The function should:
Take two inputs: bet_color and bet_amount
Return three outputs:
result_message (string saying if the bettor won or lost)
winner (0 if lost, 1 if won)
wager_message (string saying how much money was won or lost)
The payout rules are:
Red/Black → 1:1 payout
Green → 17:1 payout
If the bettor loses, they lose the amount wagered.
After that, I need to write a script that runs the function 100 times betting on "red" and calculates the odds of winning.
My issue is that I am not understanding how to get the function to be repeated multiple times and also add to a separate counter.
The error message I get is (Index exceeds the number of array elements. Index must not exceed 1.) Also, the code does not add to a counter, it instead only displays the answer one time.
This is the code for the function I made
function [result_msg,winner,wager_message] = r_wheel(bet_color, bet_amount)
disp(‘Spinning…’)
pause(2) %delay for suspense
random_int=randi([1 38]); %random # between 1 and 38
if random_int < 3 % if the # is less 1 or 2 then result is green
result_color = ‘Green’
wager_message = bet_amount*17 + bet_amount;
elseif (random_int <21) && (random_int>2)
result_color = ‘Red’ % if # is between 3 and 20 result is red
wager_message = bet_amount*2;
else
result_color = ‘Black’ %if # is between 21 and 38 the result is black
wager_message = bet_amount*2;
end
disp(result_color)
if strcmp(result_color, bet_color) % using string compare function to chekc if strings are the same
result_msg = ‘Congratulations! You win!’; % if bet color is correct set result to win
winner = 1; %set winner variable to 1
wager_message = wager_message
else
result_msg = ‘Sorry, you lose. Better luck next time!’; %if the bet color is not the same as result color set message
winner = 0; %set winner variable to 0
wager_message = -bet_amount
end
end
And here is the code for the loop.
clc, clear
x=’Red’
y= 15
win_count = 0
for i = 1:100
[result,winner]=r_wheel(x, y) % runs the function
win_count = 0
[result,winner]=r_wheel(x, y)
if winner(i)==1
win_count(i) = win_count(i)+1
else
win_count(i)= win_count(i)
end
end
disp(win_count)
disp(result) matlab code, help, error MATLAB Answers — New Questions
How can I set up Keycloak for use with MATLAB Web App Server?
I would like to set up Keycloak for authentication for MATLAB Web App Server, as I do not have my own identity provider. However, I am on Windows and cannot use the cloud reference architectures.
How do I manually set up Keycloak for authentication with MATLAB Web App Server?I would like to set up Keycloak for authentication for MATLAB Web App Server, as I do not have my own identity provider. However, I am on Windows and cannot use the cloud reference architectures.
How do I manually set up Keycloak for authentication with MATLAB Web App Server? I would like to set up Keycloak for authentication for MATLAB Web App Server, as I do not have my own identity provider. However, I am on Windows and cannot use the cloud reference architectures.
How do I manually set up Keycloak for authentication with MATLAB Web App Server? mwas, authnz MATLAB Answers — New Questions
How to Use Scoped Graph Permissions with SharePoint Lists
Enable App Access to Selected List and List Items
In the last article about scoped Graph permissions for app access to SharePoint Online and OneDrive for Business content, I discussed how to limit app access to specific files and folders. This article considers scoped permissions to lists and list items, both covered in Microsoft’s documentation about selected permissions in OneDrive and SharePoint.
Things weren’t as straightforward as dealing with files and folders. Part of this is due to the fact that the list permissions are only supported by the beta endpoint, and part is due to some documentation errors, or perhaps my understanding of what the documentation says. Anyway, let’s see how things transpired.
Adding App Access for a List
For this discussion, I use an app registration named “Limited Access to Lists” that has consent for the Lists.SelectedOperations.Selected and ListItems.SelectedOperations.Selected Graph application permissions (Figure 1). The Lists.SelectedOperations.Selected Graph permission gives an app the ability to use a scoped permission added to a list object to access the list.

To create the scoped permission, sign into an account with Sites.FullControl.All permission and populate variables with the identifiers for the application and the target site and list.
$AppId = (Get-MgApplication -Filter "displayName eq 'Limited Access to Lists").AppId $Site = Get-MgSite -Search "https://office365itpros.sharepoint.com/sites/ITComms" $List = Get-MgSiteList -SiteId $Site.Id -Filter "displayName eq 'Travel Requests'"
The next step is to construct the URI to post the Graph request to add the permission. As you can see, the URI points to the target list using the identifiers retrieved above. At the time of writing, only the beta version of the Lists endpoint supports the assignment of scoped permissions.
$Uri = ("https://graph.microsoft.com/beta/sites/{0}/lists/{1}/permissions" -f $Site.Id, $List.Id)The request body connects the app to the permission and is included in the POST request to add the scoped permission. Like the request bodies used to assign permissions to files and folders, the grantedTo property contains details of the app rather than the grantedToV2 property used by scoped site permission assignments:
$Requestbody = @{
roles = @("write") # or "read", "owner", "fullcontrol"
grantedTo = @{
application = @{
id = $AppId # Application (client) ID GUID
}
}
}
Invoke-MgGraphRequest -Uri $Uri -Method Post -Body $RequestBodyIf SharePoint Online accepts the command to create the new permission, it responds with details of the permission. To check that everything’s OK, you can use the same URI to retrieve the permissions for the list:
$Permissions = Invoke-MgGraphRequest -Uri $Uri -Method Get | Select-Object -ExpandProperty Value
You’ll find a write permission in the list of permissions. By examining the grantedToV2 property, we can see that the permission is granted to an application with the correct app identifier.
id aTowaS50fG1zLnNwLmV4dHw4NmEyMzQ1My05YWY0LTRmZDItYjEyYi02ODZjZWE3MzE2MDlAYjY2MjMxM2YtMTRmYy00M2EyLTlhN2EtZDJlMjdmNGYzNDc4
grantedToV2 {[application, System.Collections.Hashtable]}
roles {write}
$Permissions[-1].grantedToV2
Name Value
---- -----
application {[id, 86a23453-9af4-4fd2-b12b-686cea731609]}
Using Scoped App Access for a List
With the permission in place, the app can sign in access the list. The app doesn’t have consent to run Get-MgSite to enumerate or search for sites, so the site identifier might need to be hard coded. As you can see, the app can see the full set of lists in the site, including the lists used for document libraries:
$SiteId = "office365itpros.sharepoint.com,2b61a408-f05d-45b8-9d68-fb020131f86c,51ede316-f0de-4621-b315-39ce1d91d18c" Get-MgSiteList -SiteId $SiteId | Format-Table DisplayName, Id DisplayName Id ----------- -- Web Template Extensions 5feb3e71-34bb-4d87-b112-032a4e0282c7 Travel requests 04c4ef13-5245-4df1-9192-14bdca47bac3 Documents 1553d797-3e0c-4645-ac4e-b2562a2c39c5
Although the app can see the other lists, it only has permission to read items from the Travel Requests list. Here’s the code for the app to retrieve the list items:
$List = Get-MgSiteList -SiteId $SiteId -filter "displayName eq 'Travel Requests'" [array]$Data = Get-MgSiteListItem -ListId $List.Id -SiteId $SiteId
Using the techniques explained in this article, this code fetches the list items and builds a PowerShell list from the information extracted from each item:
[array]$ListItems = Get-MgSiteListItem -ListId $List.Id -SiteId $SiteId -ExpandProperty "fields(`$select=id,Linktitle,requester,reasonfortravel,destination)" -PageSize 500 -All
$ItemData = [System.Collections.Generic.List[Object]]::new()
ForEach ($Item in $ListItems.fields) {
$FullName = ($Item.AdditionalProperties.FullName)
$ReportLine = [PSCustomObject] @{
Id = $Item.Id
'Trip Title' = $Item.additionalProperties.LinkTitle
'Reason for travel' = $Item.AdditionalProperties.ReasonForTravel
Requester = $Item.AdditionalProperties.Requester
Destination = $Item.AdditionalProperties.Destination.displayName
}
$ItemData.Add($ReportLine)
}
After processing, the details of an item look like this:
Id : 1 Trip Title : Microsoft 365 Community Conference 2026 Reason for travel : Networking and learning Requester : Adele Vance Destination : Orlando
Grant App Access for a List Item
Getting even more granular, we can use much the same technique to give permission to an app for one or more items in a list. The app must have consent for the ListItems.SelectedOperations.Selected Graph permission to use item-level access.
To assign permission for a list item, the URI is built from the site and list identifiers as before with the inclusion of the list item identifier (simple integers like 1, 2, 3, and so on). Granting access is done with the same kind of POST request and request body.
$Uri = ("https://graph.microsoft.com/beta/sites/{0}/lists/{1}/items/{2}/permissions" -f $Site.Id, $List.Id, $ListItemId)
Invoke-MgGraphRequest -Uri $Uri -Method Post -Body $RequestBody
With an item-level permission in place, the app is limited to interacting with that item. All other items in the list are invisible.
Granular Access for Lists and Items
In summary, the delegated scope permissions for lists allow tenants to grant app granular levels of access to list and list items. Consider using this feature to restrict apps to accessing just the required information instead of having unfettered access to all the lists and list items in a site.
Need help to write and manage PowerShell scripts for Microsoft 365, including Azure Automation runbooks? Get a copy of the Automating Microsoft 365 with PowerShell eBook, available standalone or as part of the Office 365 for IT Pros eBook bundle.
Microsoft Sovereign Cloud adds governance, productivity and support for large AI models securely running even when completely disconnected
As digital sovereignty becomes a strategic requirement, organizations are rethinking how they deploy critical infrastructure and AI capabilities under tighter regulatory expectations and higher risk conditions. Microsoft’s approach to sovereignty is grounded in enabling enterprises, public sectors and regulated industries to participate in the digital economy securely, independently and on their own terms. The Microsoft Sovereign Cloud brings together productivity, security and cloud workloads to span both public and private environments. Customers can choose the right control posture for each workload, through a continuum of sovereign options protecting against fragmenting their architecture or increasing operational risk. Trust is built on confidence: confidence that data stays protected, controls are enforceable and operations can continue under real-world conditions.
To support these confidential environments, Microsoft offers full stack capabilities that support customers across connected, intermittently connected and fully disconnected modes. Today’s expansion of capabilities includes three major updates:
- Azure Local disconnected operations (now available) – Organizations can now run mission-critical infrastructure with Azure governance and policy control, with no cloud connectivity, optimizing continuity for sovereign, classified or isolated environments.
- Microsoft 365 Local disconnected (now available) – Core productivity workloads, Exchange Server, SharePoint Server and Skype for Business Server can run fully inside the customer’s sovereign operational boundary on Azure Local, keeping teams productive even when disconnected from the cloud.
- Foundry Local adds modern infrastructure capabilities and support for large AI models – Organizations can now bring large AI models into fully disconnected, sovereign environments with Foundry Local. Using modern infrastructure from partners like NVIDIA, customers with sovereign needs will now be able to run multimodal models locally on their own hardware, inside strict sovereign boundaries enabling powerful, local AI inferencing in fully disconnected environments.

This delivers a truly localized full stack experience built on Azure Local infrastructure and Microsoft 365 Local workloads, designed to stay resilient across any connectivity condition, with large models being part of Foundry Local extending the stack to run advanced multimodal models locally, securely, even when fully disconnected. Customers can now help maintain uninterrupted operations, keep mission critical workloads protected and apply consistent governance and policy enforcement, while keeping data, identities and operations within their sovereign boundaries.
Azure Local runs critical infrastructure locally, even when disconnected
For workloads with specialized requirements, Azure Local provides the on-premises foundation with consistent Azure governance and policy controls. With Azure Local disconnected operations, management, policy and workload execution stay within the customer-operated environments, so services continue running securely even when environments must be isolated or connectivity is not available. Using familiar Azure experiences and consistent policies, organizations can deploy and govern workloads locally without depending on continuous connection to public cloud services. Azure Local is designed to scale with mission-critical needs from smaller deployments to larger footprints that support data-intensive and AI-driven workloads. Customers can start fast, expand over time and maintain a unified operational model, all within their sovereign boundary.
Operating in disconnected environments surfaces constraints that go beyond traditional cloud assumptions: External dependencies may be unacceptable, connectivity may be intentionally restricted and operational continuity is a business imperative.
“The availability of Azure Local disconnected operations represents a breakthrough for organizations that need control over their data without sacrificing the power of the Microsoft Cloud. For Luxembourg, where digital sovereignty is not just a principle but a strategic necessity, this model offers the resilience, autonomy and trust our market expects. By combining Microsoft’s technological leadership with Proximus NXT’s sovereign cloud expertise, we are enabling our customers to innovate confidently — even in fully disconnected mode,” said Gerard Hoffmann, CEO Proximus Luxembourg.
Microsoft 365 Local keeps productivity and collaboration available in fully disconnected environments
As sovereign environments move into disconnected environments, keeping people productive becomes just as critical as keeping infrastructure online. Building on more than a decade of delivering and supporting these services, Microsoft 365 Local disconnected brings that continuity to the productivity layer, delivering Microsoft’s core server workloads — Exchange Server, SharePoint Server and Skype for Business Server supported through at least 2035 — directly into the customer’s sovereign private cloud.
With Microsoft 365 Local, teams can communicate, share information and collaborate securely within the same controlled boundary as their infrastructure and AI workloads. Everything runs locally, under customer-owned policies, with full control of data resiliency, access and compliance. By operating with Azure-consistent management and governance, customers get the productivity experience they rely on, designed to stay resilient and secure even when offline.
Bringing large models and modern infrastructure to Foundry Local
With the availability of larger models and modern infrastructure as part of the Foundry Local portfolio, Microsoft is enabling customers with highly secure environments the ability to run multimodal, large models directly inside their sovereign private cloud environments. This brings the richness of Microsoft’s enterprise AI capabilities to on-premises systems, complete with local inferencing and APIs that operate completely within customer-controlled data boundaries.
Expanding beyond small models, the integration of Foundry Local with Azure Local is specifically designed to support large-scale models utilizing the latest GPUs from partners such as NVIDIA. Microsoft will provide comprehensive support for deployments, updates and operational health. Even as inferencing demands increase over time, customers retain complete control over their data and hardware.
Choice and control without added complexity
Customers facing strict sovereignty and regulatory requirements are clear that a fully disconnected sovereign private cloud is a key business need. Microsoft Sovereign Private Cloud is designed to meet these needs head-on, enabling secure, compliant operations even in environments with no external connectivity. At the same time, we recognize that disconnected environments are not one-size-fits-all; some customers operate across connected, hybrid and disconnected modes based on mission, risk and regulation. Our approach helps customers to meet strict sovereign requirements in fully disconnected scenarios without compromising simplicity, while retaining flexibility where connectivity is possible. Together, Azure Local disconnected operations, Microsoft 365 Local and Foundry Local help organizations choose where workloads run and how environments are managed, while standardizing governance and operational practices across connected and disconnected deployments.
Get started
- Azure Local disconnected operations and Microsoft 365 Local disconnected are now available worldwide, and large models on Foundry Local are available to qualified customers.
- Explore the Microsoft Sovereign Cloud
- Learn more about Azure Local disconnected operations
Douglas Phillips leads global engineering efforts for Microsoft’s specialized, sovereign, and private clouds. He is responsible for Microsoft’s global strategy, products and operations that bring Microsoft’s industry-leading solutions, including Azure, our adaptive cloud portfolio and Microsoft 365 collaboration suite, to customers with additional sovereignty, security, edge and compliance requirements.
The post Microsoft Sovereign Cloud adds governance, productivity and support for large AI models securely running even when completely disconnected appeared first on The Official Microsoft Blog.
As digital sovereignty becomes a strategic requirement, organizations are rethinking how they deploy critical infrastructure and AI capabilities under tighter regulatory expectations and higher risk conditions. Microsoft’s approach to sovereignty is grounded in enabling enterprises, public sectors and regulated industries to participate in the digital economy securely, independently and on their own terms. The Microsoft Sovereign Cloud brings together productivity, security and cloud workloads to span both…
The post Microsoft Sovereign Cloud adds governance, productivity and support for large AI models securely running even when completely disconnected appeared first on The Official Microsoft Blog.
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