%%%% This script plots the first 500 terms of the Fourier sine series
%%%% solution to the heat equation with constant initial condition.

%%%%Parameter values are set
L=1;
k=1;

%%%%Intervals for x and t are defined
x=linspace(0,L,200);

tend=0.75;
t=linspace(0,tend,200);

%%%%Initial condition is defined
IC=23;

%%%%First 500 terms of series solution
Phi=zeros(1,200);
G=zeros(200,1);
u=zeros(200);

for j=1:2:999
    Phi=sin(j*pi*x/L);
    G=exp(-1*(j*pi/L)^2*k*t.');
    u=u+4*IC/(j*pi)*G*Phi;
end

%%%%Plot solution surface
figure(1);
surf(x,t,u); shading interp;
title('First 500 terms of Analytical Solution of Heat Equation')
xlabel('x')
ylabel('Time t')

%%%%Plot spatial distribution over time
figure(2);

for m=1:length(t)
    v=u(m,:);
    
figure(2)
plot(x,v,'-k');
title(['Solution at t=',num2str(t(m))],'fontsize',16);
xlabel('Distance x', 'fontsize',16)
ylabel('u(x)','rotation',0,'fontsize',16)
ylim([0,25]);
    
pause(0.04);
end