Direct numerical solution of Poisson`s equation in cylindrical (r, z) coordinates

A direct solver method is developed for solving Poisson`s equation numerically for the electrostatic potential {phi}(r,z) in a cylindrical region (r < R{sub wall}, 0 < z < L). The method assumes the charge density {rho}(r,z) and wall potential {phi}(r = R{sub wall}, z) are specified, and {partial_derivative}{phi}/{partial_derivative}z = 0 at the axial boundaries (z = 0, L)