'The Japan Society for Industrial and Applied Mathematics'
Doi
Abstract
In [8], the author discusses an iterative scheme for
solving 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
of the Peaceman-Rachford [10] alternating-direction operators for the Laplacian gives convergence in O(h^(-2) log h^(-1)) operations