Perturbation technique and method of fundamental solution to solve nonlinear Poisson problems

We show in this work that the Asymptotic Numerical Method (ANM) combined with the Method of Fundamental Solution (MFS) can be a robust algorithm to solve the nonlinear Poisson problem. The ANM transforms the nonlinear problem into a sequence of linear ones which can be solved by MFS. This last method consists of approximating the solution of the linear Poisson problem by a linear combination of fundamental solutions. Some examples are presented to show the efficiency of the proposed method.