Ghost point method using RBFs and polynomial basis functions

Abstract

In this paper, we propose a new Kansa method with fictitious centre approach in which the radial basis function (RBF) approximation is augmented by polynomial basis functions. The proposed approach considerably improves not only the accuracy but also the stability of the recently proposed ghost point method using radial basis functions. The difficulty of selecting a good RBF shape parameter is no longer an issue. Two numerical examples are presented to show the effectiveness and the improvement of the proposed method over previous methods.