A Boundary Integral Procedure for the Numerical Solution of a Class of Mixed Boundary-Value Problems

Abstract

A method is derived for the numerical solution of a class of boundary-value problems governed by a system of second order linear elliptic partial differential equations. The solution to a particular problem is expressed in terms of an integral taken round part of the boundary of the region under consideration. The integral equation is then solved numerically and hence the required numerical solution obtained. The method should be particularly useful for the solution of a certain class of problems in anisotropic thermostatics and elastostatics.