The Extrapolated Modified Aitken Iteration Method for Solving Elliptic Difference Equations

Abstract

This paper describes a new approach to the extrapolation (over-relaxation) and linear acceleration of the Aitken iterative method, and presents theoretical and experimental evidence concerning its application to 5-point elliptic difference equations. Comparison is made between the performance of the new method and that of existing procedures on a Laplace problem, and on a boundary-value problem in one independent variable.