High order continuation algorithm and meshless procedures to solve nonlinear Poisson problems

The paper deals with the application of Asymptotic Numerical Method (ANM) for solving non-linear Partial Differential Equations discretized by a meshless technique. In a recent paper [3], it was proposed to associate ANM and Method of Fundamental Solutions (MFS) in a boundary only framework, which permits one to compute a part of non-linear response curves up to the radius of convergence. In the present paper, a continuation algorithm is presented, that is able to compute any solution branch by using the same basis functions. The discretization technique combines fundamental solutions, method of particular solutions (referred as MPS or MFS–MPS when it is coupled with fundamental solutions) and Analog Equation Method (AEM).