The local meshless method based on Pascal polynomial basis functions for solving fourth-order PDEs. (July 2022)

• Record Type: Journal Article
• Authors: Chang, Wanru; Zhang, Jianfeng; Wang, Yun; Wang, Jiawen
• Is Part Of: Engineering analysis with boundary elements. Volume 140(2022)
• Page Start: 159
• Page End: 166
• Publication Date: 2022-07
• Subjects: Pascal polynomial basis functions -- Localized meshless method -- Fourth-order partial differential equations -- Variable coefficients; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2022.03.019
• Languages: English
• ISSNs: 0955-7997

Abstract

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.