%  Heat Diffusion in a Thin Insulated Wire

clear all; close all;
L = 1.0;                           %  Lenth of the Wire
tfinal = 1;                        %  Final Time

n = 40.; dx = L/n;                 %Number of Space Steps

rho = 1.; cond = 1/(pi*pi); spheat = 1.0;    % Material parameters

dt = dx*dx*rho*spheat/(cond*2.1);
maxk = fix(tfinal/dt),              %  Number of Time Steps

b = dt/(dx*dx); a = cond/(spheat*rho); d = a*b;

%  Initial Temperature
for i = 1:n+1
        x(i) = (i-1)*dx;
        u0(i) = sin(pi*x(i));
end

plot(x,u0); hold

t = 0;
for k=1:maxk                % Time Loop
   u1(1) = 0;
   u1(n+1) = 0;	
   for i=2:n;               % Space Loop 
      u1(i) = 0.01*dt/(spheat*rho)+(1-2*d)*u0(i) + d*(u0(i-1)+u0(i+1));
   end
   u0 = u1;   plot(x,u1)
   t = t + dt;
end

for i=1:n+1
  err(i) = u1(i)- uexact(x(i),t);
end

  figure(2); plot(x,err)
  e2 = [norm(err,1),norm(err,2),norm(err,inf)],