4620 Homework 6

You can use any programing language or tool that you want.

1) Use symetric differences in x and y to discretize

({{Δu, =, f}})

for a function f(x,y) and u on the rectangular domain Ω described by 0<x<3 and 0<y<12 using Nx subdivisions in the x direction and Ny subdivisions in the y direction. You should be able to use any number of subdivisions. Enforce a homogeneous Neumann condition on x=0, a homogeneous Dirichlet condition on x=3 and a periodic boundary condition on y=0 and y=12.

2) Find a (not-trivial) exact solution of the problem and verify that your the error in your approximation decreases as you take more subdivisions.  Hint find a function satisfying the boundary conditions (think trig for the periodic) and compute its Laplacian,  simply take that as your f.  Estimate (by plotting the error) how the error converges to zero as a function of Δx when Δx=Δy.