Numerical solutions of elliptic partial differential equations using Chebyshev polynomials. (August 2016)

• Record Type: Journal Article
• Authors: Khatri Ghimire, B.; Tian, H.Y.; Lamichhane, A.R.
• Is Part Of: Computers & mathematics with applications. Volume 72:issue 4(2016)
• Page Start: 1042
• Page End: 1054
• Publication Date: 2016-08
• Subjects: Chebyshev polynomials -- Particular solutions -- The method of fundamental solutions -- Collocation Trefftz method -- Poisson equation -- Modified Helmholtz equation; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2016.06.012
• Languages: English
• ISSNs: 0898-1221

Abstract

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.