How can I plot the following in MATLAB?

Hello Everyone! Could anyone help me plot the following Fourier Cosine series,

,

where the fourier cosine coefficients are

,

, .

I tried the following code for a specific value of n=8 just to check it but it does not give me the correct results.

clear all, clc

syms x t k

    for t=0:0.5
        bo=1.40985;
        bl=-0.443179;
        t1=exp(-(k^2)*(pi^2)*t);
        t2=k*sin(k*pi*x);
        t3=cos(k*pi*x);
        S1=symsum((bl*t1*t2),k,1,8);
        S2=symsum((bl*t1*t3),k,1,8);
        S3=bo+S2;
        S4=S1/S3;
        u=((-pi)*S4);
    end


fplot(u)

Answer 1

[David Hill]

Not sure if this is what you are looking for or not.

for n=0:8
    f=@(x)exp((1-cos(pi*x))/pi.*cos(n*pi*x));
    b(n+1)=2*integral(f,0,1);
end
b(1)=b(1)/2;
[x,t]=meshgrid(0.09:.0001:.1,0:.0001:.01);
n=zeros(size(x));
d=zeros(size(x));
for bb=2:9
    n=n+b(bb)*exp(-bb^2*pi^2*t)*bb*sin(bb*pi*x);
    d=d+b(bb)*exp(-bb^2*pi^2*t)*cos(bb*pi*x);
end
d=ones(size(x))*b(1)+d;
u=-pi*n./d;
surf(x,t,u,'EdgeColor','none');

[Haseeb Ur Rehman]

Thanks David Hill for your help. Much appreciated. I guess I am pretty much close to the desired result.

However, I would like to know that how could I plot it for and without altering the for loop for , as I want it to generate the values by adding just first 8 terms in the summation of equation. Though I tried it but I have got the error that "incorrect matrix dimensions for multiplication".

[David Hill]

for n=0:8
    f=@(x)exp((1-cos(pi*x))/pi.*cos(n*pi*x));
    b(n+1)=2*integral(f,0,1);
end
b(1)=b(1)/2;
[x,t]=meshgrid(0:.2:1,0:.02:1);
n=zeros(size(x));
d=zeros(size(x));
for bb=2:9
    n=n+b(bb)*bb*exp(-bb^2*pi^2*t).*sin(bb*pi*x);%.* element-wise
    d=d+b(bb)*exp(-bb^2*pi^2*t).*cos(bb*pi*x);%.* element-wise
end
d=ones(size(x))*b(1)+d;
u=-pi*n./d;
surf(x,t,u,'EdgeColor','none');