Title

Numerical Solutions of Elliptic Partial Differential Equations using Chebyshev Polynomials

Document Type

Article

Publication Date

8-2016

Department

Mathematics

Abstract

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.

Publication Title

Computers and Mathematics with Applications

Volume

72

Issue

4

First Page

1042

Last Page

1054

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