The local meshless method based on Pascal polynomial basis functions for solving fourth-order PDEs

Abstract

In this paper, we present a localized method based on Pascal polynomial basis functions to solve fourth-order partial differential equations (PDEs) even with variable coefficients. The proposed algorithm is simple and effective, since applying Pascal polynomial basis functions can avoid the derivation of the closed-form particular solutions for higher order PDEs. Also, the localized formulation can alleviate the ill-conditioned problem of the resulting coefficient matrix. Five numerical examples are presented to demonstrate the accuracy and effectiveness of the proposed method in both regular and irregular domains.