How to implement the Fourier series method of heat equation?

How to implement the Fourier series method of heat equation by using the same value of L,alpha,t_final,n,t0,t1s and t2s?

L=20; 
alpha=0.23; 
t_final=60; 
n=20; 
T0=20; 
T1s=100; 
T2s=0; 
dx=L/n;
dt=2;
x=dx/2:dx:L-dx/2;
t = 0:dt:t_final;
nt = length(t);
T = zeros(n, nt);
T(:,1) = T0;
for j=1:nt-1
    dTdt=zeros(n,1);
    for i=2:n-1
        dTdt(i) = alpha*(T(i+1,j)+T(i-1,j)-2*T(i,j))/dx^2;
    end
    dTdt(1) = alpha*(T(2,j)+T1s-2*T(1,j))/dx^2;
    dTdt(n) = alpha*(T2s+T(n-1,j)-2*T(n,j))/dx^2;
    T(:,j+1) = T(:,j) + dTdt*dt;
end
disp(T)
figure(1)
mesh(x,t,T.')
xlabel('Position (x)')
ylabel('Time (seconds)')
zlabel('Temparature, U(x,t)')

Answer 1

[KSSV]

You shoul dhave a look on symbolic math toolbox. Rfer this answer:

https://in.mathworks.com/matlabcentral/answers/413890-the-exact-solution-to-a-partial-differential-equation