Mathematical approach and numerical analysis to the fundamental solutions method of Dirichlet problem (Q1301923)

The author studies the solution of the Dirichlet problem in \(\mathbb{R}^2\) by the `fundamental solutions method'. It consists of choosing suitable sets of charge points \(z_{nk}\) and collocation points \(\xi_{nk}\), solving a linear system to obtain approximations of the charges at the \(z_{nk}\), and hence an approximation to the solution of the Dirichlet problem. Simple test examples are given. The paper is not easy to follow: The notation is not consistent; in the line after (5.9) the important word `not' is missing; uniform distribution of points is not invariant under linear mappings.