Some aspects of the one-dimensional version of the method of fundamental solutions

Abstract

The method of fundamental solutions (MFS) is a well-established boundary-type numerical method for the solution of certain two- and three-dimensional elliptic boundary value problems. The basic ideas were introduced by Kupradze and Alexidze, whereas the present form of the MFS was proposed by Mathon and Johnston. The aim of this work is to investigate the one-dimensional analogue of the MFS for the solution of certain two-point boundary value problems. In particular, the one-dimensional MFS is formulated in the case of linear scalar ordinary differential equations of even degree with constant coefficients. A mathematical justification for the method is provided and various aspects related to its applicability from both an analytical and a numerical standpoint are examined.