Present a finite difference discretisation on the

Question

Partial Differential Equation:

²u/x² 5(²u/y²) e^y(u/ x) cos( x 2y)

is given on the rectangle <0,3>x<-3,3>, on it's boundary u=0.

a) Present a finite difference discretisation on the equidistant square mesh.

b) How many mesh cells (as minimum) are necessary so that the matrix is diagonally dominant,

c) Present the iterative algorithm (Gauss-Seidel) allowing to solve this system.