function [x,u,ue]=myHeat2(N,dt,nstep)

% Solve the heat equation u_t = u_xx + Q(x,t)
% using centered differences in space and forward
% differences in time.  Assign Q(x,t) and ICs and
% BCs as in the class notes.

% setup mesh and initial conditions
x=linspace(0,1,N+1);
u=log(x+1);

% taken nstep time steps
t=0;
j=2:N;
dx=1/N;
r=dt/dx^2;
for n=1:nstep
  u(j)=u(j)+r*(u(j+1)-2*u(j)+u(j-1))...
    +dt*exp(-t)*((x(j)+1).^(-2)-log(x(j)+1));
  t=t+dt;
  u(1)=0;
  u(N+1)=log(2)*exp(-t);
end

% Here is the exact solution
ue=log(x+1).*exp(-t);