A Generalization of the Additive Correction Methods for the Iterative Solution of Matrix Equations

Abstract

A general formulation of the additive correction methods of Poussin [4] and Watts [7] is presented. The methods are applied to the solution of finite difference equations resulting from elliptic and parabolic partial differential equations. A new method is developed for anisotropic and heterogeneous problems. For such difficult problems the method presented here is comparable with Stone’s strongly implicit method, while all other methods tested require much greater computational effort. The correction approach discussed here can be easily applied with any iterative method.