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

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 [1,2]. The basic ideas were introduced by Kupradze and Alexidze (see, e.g., [3]), whereas the present form of the MFS was proposed by Mathon and Johnston [4]. 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.