Another Look at Iterative Methods for Elliptic Difference Equations

Abstract

Iterative methods for solving elliptic difference equations have received new attention because of the recent advent of novel computer architectures and a growing interest in three-dimensional problems. The fundamental characteristic of an iterative method is its rate of convergence. We present here, in the context of the model probelm in two and three dimensions, a very simple theory for determining the rates of convergence of block iterative schemes. This theory is easily extended to general domains, general elliptic problems, and higher dimenstions.