The method of fundamental solutions for inhomogeneous elliptic problems
Using some particular solutions of the Poisson equation or the inhomogeneous biharmonic equation, the authors transform the corresponding problems to homogeneous problems. Then they use the fundamental solutions to enforce the boundary conditions. These are satisfied in a least squares sense, namely by minimizing a nonlinear functional depending upon the unknown coefficients of the linear combination of fundamental solutions and the unknown coordinates of the sources points. However, the paper contains little discussion on any of the main topics in the numerical solution of partial differential equations, such as convergence of the discretized solution to the continuous solution, numerical stability of the computational algorithm, and error estimates of numerical solution.
scientific article; zbMATH DE number 1240671