A Practical Algorithm for Determining the Optimal Pseudo-Boundary in the Method of Fundamental Solutions

One of the main difficulties in the application of the method of funda- mental solutions (MFS)is the determination of the position of the pseudo-boundary on which are placed the singularities in terms of which the approximation is ex- pressed. In this work, we propose a simple practical algorithm for determining an estimate of the pseudo-boundary which yields the most accurate MFS approx- imation when the method is applied to certain boundary value problems. Several numerical examples are provided. AMS subject classifications: 65N35, 65N38, 65K10