function simpleFTCS_heat_animated()
 
close all
 dt = 0.0005;
  N = 25;
 fT = 0.2;
 
 x = linspace(0,1,N)';
dx = x(2) - x(1);

v = zeros(N,1);     %  solution at time level n+1
vOld = zeros(N,1);     %  solution at time level n

vOld = sin(pi*x);      % initial condition
   v = vOld;

r = dt/dx^2

t = 0;

% plot(x,vOld,'b')

ve = sin(pi.*x);

hh = plot(x,v,x,ve,'erasemode','xor');

set(hh(1),'Color',[0 0 1]);  % numerical in blue
set(hh(2),'Color',[1 0 0]);  % exact in red
set(hh(2),'LineStyle','--');
axis([0 1 -0.05 1.05]);
pause            % hit any key to continue

while t<fT
    
   for i=2:N-1
      v(i) = (1-2*r)*vOld(i) + r*(vOld(i+1) + vOld(i-1)); 
   end
   v(1) = 0;     %  apply boundary condtions
   v(N) = 0; 
   
   ve = exp(-t*pi^2).*sin(pi.*x);
   
   set(hh(1),'ydata',v)
   set(hh(2),'ydata',ve), drawnow, pause(0.01)
   
%   plot(x,v,'b',x,ve,'r'), drawnow, pause(0.01)
  
 %  axis([0 1 -0.05 1.05]);
   
   t = t + dt;
   vOld = v;
    
end

ve = exp(-t*pi^2).*sin(pi.*x);

er = norm(v-ve,inf)

% plot(x,v,'b*',x,ve,'r')