The collocation points of the fundamental solution method for the potential problem (Q1913435)

The paper is dedicated to the further development of what is called the ``fundamental solution method'' for the numerical solution of boundary value problems for elliptic equations. One discusses the Dirichlet problem for the Laplace equation. The solution of this problem as a finite set is presented via the fundamental solution. When using the fundamental solution method the difficult arises in finding the good charge and/or collocation points. A new algorithm is proposed for finding these points. One proposes to search them simultaneously with computing the constants of a set which defines the approximate solution. Numerical experiments are given, they prove the effectiveness of the developed algorithm.