How to plot analytical solution in terms of Fourier Series

Question

Muhammad Usman 2019-11-6

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https://ww2.mathworks.cn/matlabcentral/answers/489497-how-to-plot-analytical-solution-in-terms-of-fourier-series

回答： Koushik Kureti 2020-3-5

在 MATLAB Online 中打开

I want to plot the analytical solution of the equation given below:

for x=-1:1 and t=0:0.4:2 for as suitable values of p.

I tried to write the code as:

function adv_fourier()
x = linspace(-1,1);
niu=1/100*pi;
c=0.001;
% p=1;
syms n p
t=0:0.4:2;
for i=1:numel(t)
    A = @(n) (((-1)^p)*2*p*sin(p*pi*x)*exp(-niu*(p^2)*(pi^2)*t(i)))./((c^4)+8*((c*pi*niu)^2)*((p^2)+1)+16*((pi*niu)^4)*((p^2)-1)^2);
    A_sum = symsum(A(p),p,1,50);
    B = @(n) (((-1)^p)*(2*p+1)*cos(((2*p+1)/2)*pi*x)*exp(-niu*(((2*p+1)/2)^2)*(pi^2)*t(i)))/((c^4)+((c*pi*niu)^2)*(8*(p^2)+8*p+10)+((pi*niu)^4)*((4*(p^2)+4*p-3))^2);
    B_sum = symsum(B(p),p,1,50);
    S = (sinh(c/(2*niu)).*(A_sum) + cosh(c/(2*niu)).*(B_sum));
    u = 16*(pi^2)*(niu^3)*c*exp((c/(2*niu))*(x-0.5*c*t(i))).*S;
    plot(x,u);
    grid on
    hold on
end
end

But it is not genrating the desired results. Please suggest me suiable changes. Thanks

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Answer 1

Koushik Kureti 2020-3-5

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/489497-how-to-plot-analytical-solution-in-terms-of-fourier-series#answer_418638

Hello Usman,

Your MATLAB code is working all good, however, I see you are not able to generate the desired results. You can get the desired results by correcting your code at B(exponential part's denominator)as

B = @(n) (((-1)^p)*(2*p+1)*cos(((2*p+1)/2)*pi*x)*exp(-niu*(((2*p+1)/4)^2)*(pi^2)*t(i)))/((c^4)+((c*pi*niu)^2)*(8*(p^2)+8*p+10)+((pi*niu)^4)*((4*(p^2)+4*p-3))^2);

The highlighted (bold and underlined) is the correction you should make for better results.