The method of fundamental solutions for elliptic boundary value problems

The method of fundamental solutions (MFS) is a technique for the numerical solution of certain elliptic boundary value problems which falls in the class of methods generally called boundary methods. Like the boundary element method (BEM), it is applicable when a fundamental solution of the differential equation in question is known, and it shares the same advantages as the BEM over domain discretization methods. Moreover, it has certain advantages over the BEM, which will be mentioned in the following. In this paper, primary attention is devoted to the MFS solution of elliptic boundary value problems governed by equations of the form