Fully Diagonalized Chebyshev Spectral Methods for Second and Fourth Order Elliptic Boundary Value Problems
Year: 2018
Author: Jing-Min Li, Zhong-Qing Wang, Huiyuan Li
International Journal of Numerical Analysis and Modeling, Vol. 15 (2018), Iss. 1-2 : pp. 243–259
Abstract
Fully diagonalized Chebyshev spectral methods for solving second and fourth order elliptic boundary value problems are proposed. They are based on appropriate base functions for the Galerkin formulations which are complete and biorthogonal with respect to certain Sobolev inner product. The suggested base functions lead to diagonalization of discrete systems. Accordingly, both the exact solutions and the approximate solutions can be represented as infinite and truncated Fourier series. Numerical results demonstrate the effectiveness and the spectral accuracy.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2018-IJNAM-10566
International Journal of Numerical Analysis and Modeling, Vol. 15 (2018), Iss. 1-2 : pp. 243–259
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Spectral method biorthogonal Chebyshev polynomials elliptic boundary value problems numerical results.