The numerical solution of Poisson's and the bi-harmonic equations by matrices

Abstract

This note describes a simple method of solving the matrix forms of the customary families of finite difference equations which approximate to Poisson's equation (in three dimensions as well as two) and to the bi-harmonic equation. It is intended for use where the boundary of the region over which a solution is wanted is comparatively simple, that is to say, can be subdivided into a comparatively few rectangular areas or rectangular parallelepipeds.