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# How to plot analytical solution in terms of Fourier Series

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Muhammad Usman on 6 Nov 2019
Answered: Koushik Kureti on 5 Mar 2020
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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### Answers (1)

Koushik Kureti on 5 Mar 2020
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.
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