4620 Final Exam

Open book and open note!

1)  Write down a finite difference scheme for 
	(Subscript[u, t]) = β (Subscript[u, xxxx   ])
with periodic boundary conditions.

2)  Write down an explicit finite difference scheme for the heat equation
	(Subscript[u, t]) = -u + α (Subscript[u, xx])
with periodic boundary conditions and compute the LTE of the scheme.

3)  Write down an implicit finite difference scheme for the "heat like" equation
	(Subscript[u, t]) =  -u  +  α (Subscript[u, xx])
with periodic boundary conditions.

4)  Write an ADI scheme for the 2D heat equation with Dirichlet boundary conditions.  Use the "JC" as an initial condition. Perform a stability analysis on your scheme.

5)  Write an Lax-Wendroff scheme for the 1D wave equation with periodic boundary conditions.  Use any initial condition you want. Perform a stability analysis on your scheme.