Hi,
I was given a half range expansion function f(x) = 0, 0<x<2 and f(x) = 1, <2<x<4.
I was asked to solve for the Fourier cosine series and Fourier sine series and then plot each.
I solved by hand:
Fourier Cosine Series:
a0 = 1/2
an = -2/(n*pi)*sin((n*pi)/2)
f(x) = 1/2 + sum(an*cos((n*pi*x)/4)) from n =1 to infinity
Fourier Sine Series:
bn = [2/(n*pi)]*[(-1)^(n+1) + cos((n*pi)/2)]
f(x) = sum(bn*sin((n*pi*x)/4))
I’m fairly new to Matlab and very unexperienced, where I’m having dificulty is plotting these functions against x, say x = [-24 24] and n=1:1:50 or until square waves appear. I gained some experience plotting their partial sums using fplot, but that approach does not appear to work here. It isn’t feasible to plot the 50th partial sum. I’ve seen more arrayfun usage online, but I do not understand it whatsoever.
Any help and explanation would be greatly appreciated. Thanks in advance.Hi,
I was given a half range expansion function f(x) = 0, 0<x<2 and f(x) = 1, <2<x<4.
I was asked to solve for the Fourier cosine series and Fourier sine series and then plot each.
I solved by hand:
Fourier Cosine Series:
a0 = 1/2
an = -2/(n*pi)*sin((n*pi)/2)
f(x) = 1/2 + sum(an*cos((n*pi*x)/4)) from n =1 to infinity
Fourier Sine Series:
bn = [2/(n*pi)]*[(-1)^(n+1) + cos((n*pi)/2)]
f(x) = sum(bn*sin((n*pi*x)/4))
I’m fairly new to Matlab and very unexperienced, where I’m having dificulty is plotting these functions against x, say x = [-24 24] and n=1:1:50 or until square waves appear. I gained some experience plotting their partial sums using fplot, but that approach does not appear to work here. It isn’t feasible to plot the 50th partial sum. I’ve seen more arrayfun usage online, but I do not understand it whatsoever.
Any help and explanation would be greatly appreciated. Thanks in advance. Hi,
I was given a half range expansion function f(x) = 0, 0<x<2 and f(x) = 1, <2<x<4.
I was asked to solve for the Fourier cosine series and Fourier sine series and then plot each.
I solved by hand:
Fourier Cosine Series:
a0 = 1/2
an = -2/(n*pi)*sin((n*pi)/2)
f(x) = 1/2 + sum(an*cos((n*pi*x)/4)) from n =1 to infinity
Fourier Sine Series:
bn = [2/(n*pi)]*[(-1)^(n+1) + cos((n*pi)/2)]
f(x) = sum(bn*sin((n*pi*x)/4))
I’m fairly new to Matlab and very unexperienced, where I’m having dificulty is plotting these functions against x, say x = [-24 24] and n=1:1:50 or until square waves appear. I gained some experience plotting their partial sums using fplot, but that approach does not appear to work here. It isn’t feasible to plot the 50th partial sum. I’ve seen more arrayfun usage online, but I do not understand it whatsoever.
Any help and explanation would be greatly appreciated. Thanks in advance. arrays, function, time series MATLAB Answers — New Questions

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I get this error: “Unrecognized function or variable ‘mexUnwrap’” when I run my code. However, the folder containing this C++ file (mexUnwrap.c) is in my path. It also contains mexUnwrap.mexa64, mexUnwrap.mexmaci64, mexUnwrap.mexw64. Do you have any suggestions for solving this problem?I get this error: “Unrecognized function or variable ‘mexUnwrap’” when I run my code. However, the folder containing this C++ file (mexUnwrap.c) is in my path. It also contains mexUnwrap.mexa64, mexUnwrap.mexmaci64, mexUnwrap.mexw64. Do you have any suggestions for solving this problem? I get this error: “Unrecognized function or variable ‘mexUnwrap’” when I run my code. However, the folder containing this C++ file (mexUnwrap.c) is in my path. It also contains mexUnwrap.mexa64, mexUnwrap.mexmaci64, mexUnwrap.mexw64. Do you have any suggestions for solving this problem? error, unrecognized c++ function MATLAB Answers — New Questions

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I’m trying to solve an boundary value problem with eigenvalues, following the article ( https://doi.org/10.1063/5.0155331 )

where and At are certain numbers and Q() is a known function, erf function in this case.
is the unknown function and the eigenvalue.
The boundary condition is , so I specified
For small alphas my code with bvp5c works well.
However for large alphas, my solution deviates from the result in the article, and I’m encountering messages like
Warning: Results may be inaccurate because of an ill-conditioned Jacobian whose reciprocal condition number is 2.03573e-39
I guess the boundary values may be too small and tried to scale my boundary values with C*exp(-3/alpha) but the problem remains.

How can I solve the problem? Fig.1 in https://doi.org/10.1063/5.0155331 can be referred as a correct solution to this problem. My solution looks similar to it but deviates in asymptotic values.
eigenvalues0999 = zeros(1, 30);

global alpha;
global At;
options = bvpset(‘RelTol’,1e-5,’AbsTol’,1e-5);

At = 0.999;
for i=1:30
alpha=1/i;
Psi1 = 1;
solinit = bvpinit(linspace(-3,6,30000),@mat4init,Psi1);
sol = bvp5c(@mat4ode, @mat4bc, solinit,options);
eigenvalues0999(1,i) = sol.parameters;
end

figure(Color="white");
plot(eigenvalues0999);
grid on;
legend(‘0′,’0.243′,’0.5′,’0.843′,’0.999′,’FontSize’, 14)
xlabel(‘alpha^{-1}’,’FontSize’, 14);
ylabel(‘Psi’,’FontSize’, 14);
set(gca, ‘FontSize’, 14);

function dydx = mat4ode(x,y,Psi1) % equation being solved
global alpha;
global At;
dydx = [y(2)
(-alpha^2*At*2/sqrt(pi)*exp(-x.^2)*y(2)+(1+At*erf(x)-alpha*Psi1*2/sqrt(pi)*exp(-x.^2))*y(1))/(alpha^2*(1+At*erf(x)))];
end

function res = mat4bc(ya,yb,Psi1) % boundary conditions
global alpha;
res = [ya(2)-1/alpha*exp(-3/alpha)
abs(yb(1))+abs(yb(2))
%yb(2)
ya(1)-exp(-3/alpha)];
end

function yinit = mat4init(x) % initial guess function
global alpha;
yinit = [exp(-abs(x)/alpha)
-sign(x)*1/alpha*exp(-abs(x)/alpha)];
endI’m trying to solve an boundary value problem with eigenvalues, following the article ( https://doi.org/10.1063/5.0155331 )

where and At are certain numbers and Q() is a known function, erf function in this case.
is the unknown function and the eigenvalue.
The boundary condition is , so I specified
For small alphas my code with bvp5c works well.
However for large alphas, my solution deviates from the result in the article, and I’m encountering messages like
Warning: Results may be inaccurate because of an ill-conditioned Jacobian whose reciprocal condition number is 2.03573e-39
I guess the boundary values may be too small and tried to scale my boundary values with C*exp(-3/alpha) but the problem remains.

How can I solve the problem? Fig.1 in https://doi.org/10.1063/5.0155331 can be referred as a correct solution to this problem. My solution looks similar to it but deviates in asymptotic values.
eigenvalues0999 = zeros(1, 30);

global alpha;
global At;
options = bvpset(‘RelTol’,1e-5,’AbsTol’,1e-5);

At = 0.999;
for i=1:30
alpha=1/i;
Psi1 = 1;
solinit = bvpinit(linspace(-3,6,30000),@mat4init,Psi1);
sol = bvp5c(@mat4ode, @mat4bc, solinit,options);
eigenvalues0999(1,i) = sol.parameters;
end

figure(Color="white");
plot(eigenvalues0999);
grid on;
legend(‘0′,’0.243′,’0.5′,’0.843′,’0.999′,’FontSize’, 14)
xlabel(‘alpha^{-1}’,’FontSize’, 14);
ylabel(‘Psi’,’FontSize’, 14);
set(gca, ‘FontSize’, 14);

function dydx = mat4ode(x,y,Psi1) % equation being solved
global alpha;
global At;
dydx = [y(2)
(-alpha^2*At*2/sqrt(pi)*exp(-x.^2)*y(2)+(1+At*erf(x)-alpha*Psi1*2/sqrt(pi)*exp(-x.^2))*y(1))/(alpha^2*(1+At*erf(x)))];
end

function res = mat4bc(ya,yb,Psi1) % boundary conditions
global alpha;
res = [ya(2)-1/alpha*exp(-3/alpha)
abs(yb(1))+abs(yb(2))
%yb(2)
ya(1)-exp(-3/alpha)];
end

function yinit = mat4init(x) % initial guess function
global alpha;
yinit = [exp(-abs(x)/alpha)
-sign(x)*1/alpha*exp(-abs(x)/alpha)];
end I’m trying to solve an boundary value problem with eigenvalues, following the article ( https://doi.org/10.1063/5.0155331 )

where and At are certain numbers and Q() is a known function, erf function in this case.
is the unknown function and the eigenvalue.
The boundary condition is , so I specified
For small alphas my code with bvp5c works well.
However for large alphas, my solution deviates from the result in the article, and I’m encountering messages like
Warning: Results may be inaccurate because of an ill-conditioned Jacobian whose reciprocal condition number is 2.03573e-39
I guess the boundary values may be too small and tried to scale my boundary values with C*exp(-3/alpha) but the problem remains.

How can I solve the problem? Fig.1 in https://doi.org/10.1063/5.0155331 can be referred as a correct solution to this problem. My solution looks similar to it but deviates in asymptotic values.
eigenvalues0999 = zeros(1, 30);

global alpha;
global At;
options = bvpset(‘RelTol’,1e-5,’AbsTol’,1e-5);

At = 0.999;
for i=1:30
alpha=1/i;
Psi1 = 1;
solinit = bvpinit(linspace(-3,6,30000),@mat4init,Psi1);
sol = bvp5c(@mat4ode, @mat4bc, solinit,options);
eigenvalues0999(1,i) = sol.parameters;
end

figure(Color="white");
plot(eigenvalues0999);
grid on;
legend(‘0′,’0.243′,’0.5′,’0.843′,’0.999′,’FontSize’, 14)
xlabel(‘alpha^{-1}’,’FontSize’, 14);
ylabel(‘Psi’,’FontSize’, 14);
set(gca, ‘FontSize’, 14);

function dydx = mat4ode(x,y,Psi1) % equation being solved
global alpha;
global At;
dydx = [y(2)
(-alpha^2*At*2/sqrt(pi)*exp(-x.^2)*y(2)+(1+At*erf(x)-alpha*Psi1*2/sqrt(pi)*exp(-x.^2))*y(1))/(alpha^2*(1+At*erf(x)))];
end

function res = mat4bc(ya,yb,Psi1) % boundary conditions
global alpha;
res = [ya(2)-1/alpha*exp(-3/alpha)
abs(yb(1))+abs(yb(2))
%yb(2)
ya(1)-exp(-3/alpha)];
end

function yinit = mat4init(x) % initial guess function
global alpha;
yinit = [exp(-abs(x)/alpha)
-sign(x)*1/alpha*exp(-abs(x)/alpha)];
end bvp5c, solve MATLAB Answers — New Questions

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Modify the Task 2 & 7 section of the script so that it performs the red shift calculation on the second star in spectra, not the sixth.
I have changed s to the second column (s= spectra(:,2)), and that is right.
How do I get the correct values of lambdaHa and speed?Modify the Task 2 & 7 section of the script so that it performs the red shift calculation on the second star in spectra, not the sixth.
I have changed s to the second column (s= spectra(:,2)), and that is right.
How do I get the correct values of lambdaHa and speed? Modify the Task 2 & 7 section of the script so that it performs the red shift calculation on the second star in spectra, not the sixth.
I have changed s to the second column (s= spectra(:,2)), and that is right.
How do I get the correct values of lambdaHa and speed? onramp, stellar motion 14.1, inramp, stellar motion MATLAB Answers — New Questions

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