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

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.