HWK 3, Due Tue May 2
Make your write-up clean and concise. I do not need to see all you algebra. Imagine that you are writing an example for a book. The main steps have to come out clearly but all the details should not be shown.

[Strikwerda 14.3.1] Use the conjugate gradient method to solve Poisson's equation uxx + uyy = -4 cos(x+y) sin(x-y) on the unit square. The boundary conditions and exact solution are given by u = cos(x+y) sin(x-y). Use the standard five-point difference sheme with h = dx=dy=0.1, 0.25, 0.025. The initial iterate should be zero in the interior of the square. Comment on the accuracy of the scheme and the efficiency of the method. Stop the iterative method when the L2 norm of the change is less than 10-6.