Numerical solutions of elliptic partial differential equations using Chebyshev polynomials

被引：24

作者：

Ghimire, B. Khatri ^{[1
]}

Tian, H. Y. ^{[1
]}

Lamichhane, A. R. ^{[1
]}

机构：

[1] Univ Southern Mississippi, Dept Math, Hattiesburg, MS 39406 USA

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2016年 / 72卷 / 04期

关键词：

Chebyshev polynomials; Particular solutions; The method of fundamental solutions; Collocation Trefftz method; Poisson equation; Modified Helmholtz equation; FUNDAMENTAL-SOLUTIONS; TREFFTZ METHOD; HELMHOLTZ-TYPE; OPERATORS;

D O I：

10.1016/j.camwa.2016.06.012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a simple and effective Chebyshev polynomial scheme (CPS) combined with the method of fundamental solutions (MFS) and the equilibrated collocation Trefftz method for the numerical solutions of inhomogeneous elliptic partial differential equations (PDEs). In this paper, CPS is applied in a two-step approach. First, Chebyshev polynomials are used to approximate a particular solution of a PDE. Chebyshev nodes which are the roots of Chebyshev polynomials are used in the polynomial interpolation due to its spectral convergence. Then the resulting homogeneous equation is solved by boundary type methods including the MFS and the equilibrated collocation Trefftz method. Numerical results for problems on various irregular domains show that our proposed scheme is highly accurate and efficient. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：1042 / 1054

页数：13

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