on Poisson eq solution

yfyap

i am trying to solve a poisson equation:

d^2/dx^2(PHI) + d^2/dy^2(PHI) = S

where S is a modified source term that satisfy the consequence of Green Thereom. the boundary conditions are the Neumann type, where at the boundary:

the normal derivative of PHI=0, i.e. d(PHI)/dn=0

By utilizing ADI, solution is obtained. but the problem is when i substitute the solution to check if the boundary conditions are satisfied, it turns out that :

d(PHI)/dn <> 0 (not equal to)

the question are: what can be the possible cause? how can this problem be tackled?

any advice is appreciated. regards, yfyap