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

被引：3

作者：

Chang, Wanru ^{[1
]}

Zhang, Jianfeng ^{[2
]}

Wang, Yun ^{[1
]}

Wang, Jiawen ^{[1
]}

机构：

[1] Zhejiang Univ, Sch Math Sci, Hangzhou, Peoples R China

[2] Zhejiang Normal Univ, Coll Math Med, Jinhua, Peoples R China

来源：

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS | 2022年 / 140卷

基金：

中国国家自然科学基金;

关键词：

Pascal polynomial basis functions; Localized meshless method; Fourth-order partial differential equations; Variable coefficients; FUNCTION COLLOCATION METHOD; FUNDAMENTAL-SOLUTIONS; PLATE; EQUATIONS;

D O I：

10.1016/j.enganabound.2022.03.019

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

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.

引用

页码：159 / 166

页数：8

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