function [x,u,ue]=myHeat3(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
dx=1/N;
x=linspace(-dx,1+dx,N+3);
u=log(x+1);

% taken nstep time steps
t=0;
j=2:N+2;
r=dt/dx^2;
for n=1:nstep
  Q=exp(-t)*((x(j)+1).^(-2)-log(x(j)+1));
  u(j)=u(j)+r*(u(j+1)-2*u(j)+u(j-1))+dt*Q;
  t=t+dt;
  u(1)=u(3)-2*dx*exp(-t);
  u(N+3)=u(N+1)+2*dx*exp(-t)/2;
end

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