function heatmovie(tf);
% HEATMOVIE Produces "movie" of exact (Fourier) soln
% of heat equation problem.
% Example:
%   >> heatmovie(0.02)
%   >> heatmovie(0.0005)
% ELB 2/21/05

xx=linspace(0,1,2000); 
MM=20; % number of movie frames
for j = 1:MM+1
    t=tf*(j-1)/MM;  plot(xx,exactsoln(xx,t))
    axis([0 1 -12 12]), xlabel x, ylabel u, grid on
    set(gca,'nextplot','replacechildren');
    legend(['t= ' num2str(t)])
    F(j) = getframe;
end
movie(F,2) % play the movie three times total


function u=exactsoln(x,t);
% subfunction to compute the exact soln
N=500; m=1:N; a=zeros(1,N);
a(3)=2/3; a(33)=10/3;
mm=m((m~=3)&(m~=33));
temp=10*(sin((33-mm)*pi/3)./((33-mm)*pi)-sin((33+mm)*pi/3)./((33+mm)*pi));
a(mm)=temp+sin((3+mm)*pi/3)./((3+mm)*pi) - sin((3-mm)*pi/3)./((3-mm)*pi);
pim=pi*(1:N);  ae=a.*exp(-t*(pim.^2));
u=sum(repmat(ae',1,length(x)).*sin(pim'*x));