On taylor expansion methods for multivariate integral equations of the second kind

Abstract

A new Taylor series method that the authors originally developed for the solution of one-dimensional integral equations is extended to solve multivariate integral equations. In this paper, the new method is applied to the solution of multivariate Fredholm equations of the second kind. A comparison is given of the new method and the traditional Taylor series method of solving integral equations. The new method is adapted to parallel computation and can therefore be highly efficient on modern computers. The method also gives highly accurate approximations for all derivatives of the solution up to the order of the Taylor series approximation. Numerical examples are given to illustrate the efficiency and accuracy of the method.