bvp4c problem with fewer boundary value than variable
In my problem i have 11 varaible of y but only 9 boundary conditions what can i do here? Another additional problem is equation 3 and 4 both contain θ₂ and φ₂ how do i write y9′ and y11′ for them? in my code i took one of the constant as zero. I also tried taking some other boundary condition (f” and f”)=0 to solve it but solution is unstable.
clc;clear;
work=0;
nnn=0;
aa=.5;
bb=10;
cc=30;
name=’B’;
sol=main(aa,bb,cc,name);
function sol1=main(aa,bb,cc,name)
sol=jobs(aa);
% sol1=jobs(bb);
% sol2=jobs(cc);
figure(‘Name’,name)
hold on
subplot(2,2,1)
plotting(2,"Pimary Velocity(F’)",sol,cc)%,sol1,sol2,aa,bb,
subplot(2,2,2)
plotting(5,"Secondary Velocity(G)",sol,cc)
subplot(2,2,3)
plotting(8,"Concentation 1 (Xi)",sol,cc)
subplot(2,2,4)
plotting(10,"Temparature(Theta)",sol,cc)
xlim([0 3.2])
hold off
sol1=sol;
end
function plotting(line,titles,sol,aa)%,sol1,sol2,aa,bb,cc
hold on
grid on
a=plot(sol.x,sol.y(line,:),’r’);
% b=plot(sol1.x,sol1.y(line,:),’g’);
% c=plot(sol2.x,sol2.y(line,:),’b’);
xline(0);
yline(0);
% legend([a; b; c],{num2str(aa); num2str(bb) ;num2str(cc)})
title(titles)
hold off
end
function out=jobs(VARABLE)
RC=.1;FW=.5;
M=0.5;BI =1.5;BE = 1.5;AE = 1+BE*BI;R=0.6;GR=8;
GM=6;PR=.71;EC=0.3; S = 0.5;S0 = 1;K=.5;SC=.6;
D = 2;GAMMA = 1;EPS = .8;ST = 5;STT= .5;
NEBLA = 2;LAMB=.8;short=AE^2+BE^2;XX=1+D;W1=1.5;CP=1.5;DF=.8;n=.01;
sol1 = bvpinit(linspace(0,1,500),[1 1 1 1 1 0 0 0 0 0 1]);
sol = bvp4c(@bvp2d, @bc2d, sol1);
sol1=bvpinit(sol,[0 10]);
sol = bvp4c(@bvp2d, @bc2d, sol1);
% sol1=bvpinit(sol,[0 2]);
% sol = bvp4c(@bvp2d, @bc2d, sol1);
out=sol;
function yvector =bvp2d(~,y)
% if y(1)==0
% y(1)=0.01;
% end
yy4=(-y(4)-y(3)*y(1)-W1*(2*y(4)*y(2)+y(3)^2)+K*y(2)+(M/(AE^2+BE^2))*…
(AE*y(2)+BE*y(5))+R*y(5)-GAMMA*y(2)^2+GM*y(10)+GR*y(8))/(-W1*y(1));
yy7=(-y(1)*y(6)-y(7)-2*W1*y(2)*y(7)+K*y(5)-(M/short)*(AE*y(5)+…
BE*y(2))+R*y(2)+GAMMA*y(5)^2)/(W1*y(1));
% yy11=(y(1)*y(9)-y(1)*y(11)*DF*SC+(EC/CP)*(y(3)^2+y(6)^2)+…
% (M*EC)/short*(y(2)^2+y(5)^2)+RC-DF*SC*(y(10)+1))/(1/PR-DF*S0*SC);
% yy9=(y(1)*y(9)+EC/CP*(y(3)^2+y(6)^2)+M*EC/short*(y(2)^2+y(5)^2))/(-PR);
% yy11=(-y(1)*y(11)-S0*yy9-RC*y(10))*SC;
yy11=(-y(1)*y(11)+RC*y(10))*SC;
yy9=(y(1)*y(9)+EC/CP*(y(3)^2+y(6)^2)+M*EC/short*(y(2)^2+y(5)^2)+DF*yy11)/(-PR);
yvector=[y(2);y(3);y(4);yy4;y(6);y(7);yy7;y(9);yy9;y(11);yy11];
end
function residual=bc2d(y0,yinf)
residual=[y0(1)-FW;y0(2)-1;y0(5);y0(8)-1;y0(10)-1;yinf(3);yinf(4);
yinf(2);yinf(5);yinf(8);yinf(10)];
end
endIn my problem i have 11 varaible of y but only 9 boundary conditions what can i do here? Another additional problem is equation 3 and 4 both contain θ₂ and φ₂ how do i write y9′ and y11′ for them? in my code i took one of the constant as zero. I also tried taking some other boundary condition (f” and f”)=0 to solve it but solution is unstable.
clc;clear;
work=0;
nnn=0;
aa=.5;
bb=10;
cc=30;
name=’B’;
sol=main(aa,bb,cc,name);
function sol1=main(aa,bb,cc,name)
sol=jobs(aa);
% sol1=jobs(bb);
% sol2=jobs(cc);
figure(‘Name’,name)
hold on
subplot(2,2,1)
plotting(2,"Pimary Velocity(F’)",sol,cc)%,sol1,sol2,aa,bb,
subplot(2,2,2)
plotting(5,"Secondary Velocity(G)",sol,cc)
subplot(2,2,3)
plotting(8,"Concentation 1 (Xi)",sol,cc)
subplot(2,2,4)
plotting(10,"Temparature(Theta)",sol,cc)
xlim([0 3.2])
hold off
sol1=sol;
end
function plotting(line,titles,sol,aa)%,sol1,sol2,aa,bb,cc
hold on
grid on
a=plot(sol.x,sol.y(line,:),’r’);
% b=plot(sol1.x,sol1.y(line,:),’g’);
% c=plot(sol2.x,sol2.y(line,:),’b’);
xline(0);
yline(0);
% legend([a; b; c],{num2str(aa); num2str(bb) ;num2str(cc)})
title(titles)
hold off
end
function out=jobs(VARABLE)
RC=.1;FW=.5;
M=0.5;BI =1.5;BE = 1.5;AE = 1+BE*BI;R=0.6;GR=8;
GM=6;PR=.71;EC=0.3; S = 0.5;S0 = 1;K=.5;SC=.6;
D = 2;GAMMA = 1;EPS = .8;ST = 5;STT= .5;
NEBLA = 2;LAMB=.8;short=AE^2+BE^2;XX=1+D;W1=1.5;CP=1.5;DF=.8;n=.01;
sol1 = bvpinit(linspace(0,1,500),[1 1 1 1 1 0 0 0 0 0 1]);
sol = bvp4c(@bvp2d, @bc2d, sol1);
sol1=bvpinit(sol,[0 10]);
sol = bvp4c(@bvp2d, @bc2d, sol1);
% sol1=bvpinit(sol,[0 2]);
% sol = bvp4c(@bvp2d, @bc2d, sol1);
out=sol;
function yvector =bvp2d(~,y)
% if y(1)==0
% y(1)=0.01;
% end
yy4=(-y(4)-y(3)*y(1)-W1*(2*y(4)*y(2)+y(3)^2)+K*y(2)+(M/(AE^2+BE^2))*…
(AE*y(2)+BE*y(5))+R*y(5)-GAMMA*y(2)^2+GM*y(10)+GR*y(8))/(-W1*y(1));
yy7=(-y(1)*y(6)-y(7)-2*W1*y(2)*y(7)+K*y(5)-(M/short)*(AE*y(5)+…
BE*y(2))+R*y(2)+GAMMA*y(5)^2)/(W1*y(1));
% yy11=(y(1)*y(9)-y(1)*y(11)*DF*SC+(EC/CP)*(y(3)^2+y(6)^2)+…
% (M*EC)/short*(y(2)^2+y(5)^2)+RC-DF*SC*(y(10)+1))/(1/PR-DF*S0*SC);
% yy9=(y(1)*y(9)+EC/CP*(y(3)^2+y(6)^2)+M*EC/short*(y(2)^2+y(5)^2))/(-PR);
% yy11=(-y(1)*y(11)-S0*yy9-RC*y(10))*SC;
yy11=(-y(1)*y(11)+RC*y(10))*SC;
yy9=(y(1)*y(9)+EC/CP*(y(3)^2+y(6)^2)+M*EC/short*(y(2)^2+y(5)^2)+DF*yy11)/(-PR);
yvector=[y(2);y(3);y(4);yy4;y(6);y(7);yy7;y(9);yy9;y(11);yy11];
end
function residual=bc2d(y0,yinf)
residual=[y0(1)-FW;y0(2)-1;y0(5);y0(8)-1;y0(10)-1;yinf(3);yinf(4);
yinf(2);yinf(5);yinf(8);yinf(10)];
end
end In my problem i have 11 varaible of y but only 9 boundary conditions what can i do here? Another additional problem is equation 3 and 4 both contain θ₂ and φ₂ how do i write y9′ and y11′ for them? in my code i took one of the constant as zero. I also tried taking some other boundary condition (f” and f”)=0 to solve it but solution is unstable.
clc;clear;
work=0;
nnn=0;
aa=.5;
bb=10;
cc=30;
name=’B’;
sol=main(aa,bb,cc,name);
function sol1=main(aa,bb,cc,name)
sol=jobs(aa);
% sol1=jobs(bb);
% sol2=jobs(cc);
figure(‘Name’,name)
hold on
subplot(2,2,1)
plotting(2,"Pimary Velocity(F’)",sol,cc)%,sol1,sol2,aa,bb,
subplot(2,2,2)
plotting(5,"Secondary Velocity(G)",sol,cc)
subplot(2,2,3)
plotting(8,"Concentation 1 (Xi)",sol,cc)
subplot(2,2,4)
plotting(10,"Temparature(Theta)",sol,cc)
xlim([0 3.2])
hold off
sol1=sol;
end
function plotting(line,titles,sol,aa)%,sol1,sol2,aa,bb,cc
hold on
grid on
a=plot(sol.x,sol.y(line,:),’r’);
% b=plot(sol1.x,sol1.y(line,:),’g’);
% c=plot(sol2.x,sol2.y(line,:),’b’);
xline(0);
yline(0);
% legend([a; b; c],{num2str(aa); num2str(bb) ;num2str(cc)})
title(titles)
hold off
end
function out=jobs(VARABLE)
RC=.1;FW=.5;
M=0.5;BI =1.5;BE = 1.5;AE = 1+BE*BI;R=0.6;GR=8;
GM=6;PR=.71;EC=0.3; S = 0.5;S0 = 1;K=.5;SC=.6;
D = 2;GAMMA = 1;EPS = .8;ST = 5;STT= .5;
NEBLA = 2;LAMB=.8;short=AE^2+BE^2;XX=1+D;W1=1.5;CP=1.5;DF=.8;n=.01;
sol1 = bvpinit(linspace(0,1,500),[1 1 1 1 1 0 0 0 0 0 1]);
sol = bvp4c(@bvp2d, @bc2d, sol1);
sol1=bvpinit(sol,[0 10]);
sol = bvp4c(@bvp2d, @bc2d, sol1);
% sol1=bvpinit(sol,[0 2]);
% sol = bvp4c(@bvp2d, @bc2d, sol1);
out=sol;
function yvector =bvp2d(~,y)
% if y(1)==0
% y(1)=0.01;
% end
yy4=(-y(4)-y(3)*y(1)-W1*(2*y(4)*y(2)+y(3)^2)+K*y(2)+(M/(AE^2+BE^2))*…
(AE*y(2)+BE*y(5))+R*y(5)-GAMMA*y(2)^2+GM*y(10)+GR*y(8))/(-W1*y(1));
yy7=(-y(1)*y(6)-y(7)-2*W1*y(2)*y(7)+K*y(5)-(M/short)*(AE*y(5)+…
BE*y(2))+R*y(2)+GAMMA*y(5)^2)/(W1*y(1));
% yy11=(y(1)*y(9)-y(1)*y(11)*DF*SC+(EC/CP)*(y(3)^2+y(6)^2)+…
% (M*EC)/short*(y(2)^2+y(5)^2)+RC-DF*SC*(y(10)+1))/(1/PR-DF*S0*SC);
% yy9=(y(1)*y(9)+EC/CP*(y(3)^2+y(6)^2)+M*EC/short*(y(2)^2+y(5)^2))/(-PR);
% yy11=(-y(1)*y(11)-S0*yy9-RC*y(10))*SC;
yy11=(-y(1)*y(11)+RC*y(10))*SC;
yy9=(y(1)*y(9)+EC/CP*(y(3)^2+y(6)^2)+M*EC/short*(y(2)^2+y(5)^2)+DF*yy11)/(-PR);
yvector=[y(2);y(3);y(4);yy4;y(6);y(7);yy7;y(9);yy9;y(11);yy11];
end
function residual=bc2d(y0,yinf)
residual=[y0(1)-FW;y0(2)-1;y0(5);y0(8)-1;y0(10)-1;yinf(3);yinf(4);
yinf(2);yinf(5);yinf(8);yinf(10)];
end
end bvp4c, steady fluid MATLAB Answers — New Questions