The Solution of Elliptic Difference Equations by Semi-Explicit Iterative Techniques

In [8], the author discusses an iterative scheme for a difference analogue for the elliptic differential equation ∇•α∇u = f on two-dimensional rectangular regions with Dirichlet boundary conditions. It is shown there that a semi-explicit technique involving the inversion only the Peaceman-Rachford [10] alternating-direction operators for the Laplacian gives convergence in O(h^(-2) log h^(-1)) operations.