function [x,U] = pdeproblem(N,T)

   dx = (1-0)/N;
   x = dx*[0:N];
   dt = dx*dx/2.0;
   
   U(1,:) = cos(2*pi*x);
   for n = 1:T,
      U(n+1,2:N) = U(n,2:N)+dt*(U(n,3:N+1)-2*U(n,2:N)+U(n,1:N-1))/(dx*dx);
      U(n+1,1) = 1;
      U(n+1,N+1) = 1;
   end