ODE solution using Fourier series

Question

Muhammad Usman 2021-5-16

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/831383-ode-solution-using-fourier-series

回答： Jan 2021-5-16

在 MATLAB Online 中打开

Hello,

I am trying to solve first order ode (

) using Fourier Series. I wrote the code, but I was doing something, please idetify my mistake.

Fourier series:

by putting into original ODE. Here's the code:

clear all;clc;close all;
syms x
N = 3;
for j=1:(2*N+1)
    xp(j) = simplify(-sym(pi) + (2*sym(pi)*(j-1))./(2.*N+1)); % Equidistance points
    end
for k = 1:2*N+1
    for l =1:N
    a(k,l) = cos(l*xp(k));
    b(k,l) = sin(l*xp(k));
    end
end
one_col = ones(1,2*N+1);
sumab = double([a';b']);
A = (1+cos(x)).*double([one_col;sumab])'
x = (A\ones(7,1))
a0 = x(1);
an = x(2:N+1);
bn = x(N+2:2*N+1);
dA = diff(A);
% ODE
A_ODE = dA + A;
yxp = A_ODE*x
plot(xp,yxp);
hold on;
%% ODE45
[a,b] = ode45(@(a,b) -(1+cos(a))*b+1, [0 30],0); %to distinguish variable I choose x = a and y = b
plot(a,b)

Thanks

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Jan 2021-5-16

Please mention, why you assume, that there is a mistake. You d have this important information already. Then it is useful to share it with the ones, who want to help you.

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Answer 1

Jan 2021-5-16

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/831383-ode-solution-using-fourier-series#answer_700898

在 MATLAB Online 中打开

syms x

N = 3;

for j=1:(2*N+1)

xp(j) = simplify(-sym(pi) + (2*sym(pi)*(j-1))./(2.*N+1)); % Equidistance points

end

for k = 1:2*N+1

for l =1:N

a(k,l) = cos(l*xp(k));

b(k,l) = sin(l*xp(k));

end

one_col = ones(1,2*N+1);

sumab = double([a';b']);

A = (1+cos(x)).*double([one_col;sumab])'

A =

x = (A\ones(7,1))

x =

Are you sure that this is wanted?

a0 = x(1);

an = x(2:N+1);

bn = x(N+2:2*N+1);

dA = diff(A);

% ODE

A_ODE = dA + A;

yxp = A_ODE*x

yxp =

plot(xp,yxp);

Error using plot
Data must be numeric, datetime, duration or an array convertible to double.

hold on;

%% ODE45

[a,b] = ode45(@(a,b) -(1+cos(a))*b+1, [0 30],0); %to distinguish variable I choose x = a and y = b

plot(a,b)

Your code does not contain meaningful comments. Guessing its intention is not reliable. Therefore it is hard to estimate, if something is wanted or a mistake.