Comparison between RBF and FDM for solving nonlinear time-dependent PDEs using Newton’s Method

Abstract

Abstract In this paper, the improved localized method of approximated particular solutions (ILMAPS) using polyharmonic splines with constant polynomial basis is used to approximate solutions of nonlinear time-dependent PDEs. The discretization process is done through a simple implicit time stepping and a collocation technique on a set of points in local domains of influence. Resulted system of nonlinear algebraic equations is solved by Newton’s method. Numerical experiments suggest that the proposed method yields superior accuracy than other RBFs as well as FDM for solving nonlinear PDEs.