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
Recommended Citation
Ghimire, B.,
Tian, H.,
Lamichhane, A.
(2016). Numerical Solutions of Elliptic Partial Differential Equations using Chebyshev Polynomials. Computers and Mathematics with Applications, 72(4), 1042-1054.
Available at: https://aquila.usm.edu/fac_pubs/17434