4620 Homework 6

1) Implement and document a 2D version of CN for 
	(Subscript[u, t])=(Subscript[u, xx])+(Subscript[u, yy])+f[x,y]
on the domain 0<x<2 and 3<y<4 with periodic boundary conditions 
	u[x,3,t]=u[x,4,t]
and non-homogeneous dirichlet conditions
	u[0,y,t]=fd[y,t]
and non-homogeneous Neumann conditions
	(Subscript[u, x])[2,y,t]=fn[y,t]
 You code needs to be able to change nx,ny and Δt and be run for various input functions f, fd, and fn.

2) Test your code on a know solution by picking any u satisfying the periodicity and picking the input functions so that it works. Make sure your code reproduces your chose solution.

3) Illustrate that the convergence of your numerical solution on your test problem.