Consider the Poisson equation uxx uyy 16x1xy1y 0 x 1 0

Consider the Poisson equation

u_xx + u_yy = 16x(1-x)y(1-y), 0 < x < 1, 0 < y < 1

with boundary conditions: u(x,0) = u(x,1) = u(0,y) = u(1,y) = 0

Write down a discretization of this problem based on the 5-point Laplacian.

Solution

http://mcs258.cankaya.edu.tr/uploads/files/258LecNot.pdf