% Script for testing the Implicit Euler method for the heat equation

u   = @(x,t)  (1+x).^3.*(1+t.^2);
f   = @(x,t)  (1+x).^3*2.*t-6*(1+x).*(1+t.^2);
g0  = @(t) 1+t.^2;
g1  = @(t) 8*(1+t.^2);
v   = @(x) (1+x).^3;

M=5; MT=10;    
for i=1:5
    [U,X,T]=heatImplEuler(2,f,v,g0,g1,M,MT);
    Err = U - u(X,T);
    error(i)=max(abs(Err(:)));
    M=2*M;
    MT=4*MT;   
end