In this paper we give an overview of the Method of Fundamental Solutions (MFS) as a
heuristic numerical method. It is truly meshless. Its concept and numerical implementation …

The method of fundamental solutions (MFS) may be seen as one of the simplest methods for
solving boundary value problems for some linear partial differential equations (PDEs). It is a …

In this paper, we consider the accuracy and stability of implementing the method of
fundamental solutions. In contrast to the results shown in [5], we find that Gaussian …

We show how to extend the method of fundamental solutions (MFS) to solve Poisson's
equation in R2 and R2 without boundary or domain discretization. To do this an approximate …

The method of fundamental solutions (MFS) is a popular tool to solve Laplace and
Helmholtz boundary value problems. Its main drawback is that it often leads to ill …

In this work, the use of the Method of Fundamental Solutions (MFS) for solving elliptic partial
differential equations is investigated, and the performance of various least squares routines …

The method of fundamental solutions (MFS) is a relatively new method for the numerical
solution of boundary value problems and initial/boundary value problems governed by …

For the method of fundamental solutions (MFS), a trial solution is expressed as a linear
combination of fundamental solutions. However, the accuracy of MFS is heavily dependent …

The classical method of fundamental solutions (MFS) has only been used to approximate
the solution of homogeneous PDE problems. Coupled with other numerical schemes such …

This paper proposes a novel meshless boundary method called the singular boundary
method (SBM). This method is mathematically simple, easy-to-program, and truly meshless …