An Integral Equation Method for Solving Mixed Boundary Value Problems

The representation formula which embodies the solution of a two-part or a three-part mixed boundary value problem leads to a Fredholm integral equation of the first kind which cannot be solved easily. In this paper we present a technique which reduces the Fredholm integral equation of the first kind to Volterra integral equations of the first kind and Fredholm integral equations of the second kind. The Volterra integral equations have a rather simple kernel and can therefore be readily inverted, while the Fredholm integral equations of the second kind can be solved by the method of successive approximations. Each section of the paper is illustrated by an appropriate example.