Convergence and stability of the method of meshless fundamental solutions using an array of randomly distributed sources
The authors consider the Laplace equation in two-dimensional simply connected bounded domain under the Dirichlet and Neumann conditions on parts of the boundary. They discuss applications of a variant of collocation method on the boundary which makes use of several external source functions. They write about a possibility to obtain an over-determined system but almost everywhere they consider only the case when the corresponding matrix is invertible and ``a solution is assured if rational or symbolic computation is used throughout''. Results dealing with convergence relate to the moving the sources ``a sufficient distance from the boundary''. But there are words about possible great round-off errors. Numerical examples with simple domains and a relatively small number of sources are discussed. Special attention is paid to the case of randomly distributed sources.
scientific article; zbMATH DE number 2102403