Year: 2018
Author: Xuhong Yu, Yunge Zhao, Zhongqing Wang
Journal of Mathematical Study, Vol. 51 (2018), Iss. 2 : pp. 196–213
Abstract
A diagonalized Legendre rational spectral method for solving second and fourth order differential equations are proposed. Some Fourier-like Sobolev orthogonal basis functions are constructed which lead to the 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 of this approach.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v51n2.18.05
Journal of Mathematical Study, Vol. 51 (2018), Iss. 2 : pp. 196–213
Published online: 2018-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Legendre rational spectral method Sobolev orthogonal functions elliptic boundary value problems heat equation numerical results.
Author Details
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Diagonalized Gegenbauer rational spectral methods for second- and fourth-order problems on the whole line
Li, Shan
Lai, Zhenyan
Jin, Lusha
Yu, Xuhong
Applied Numerical Mathematics, Vol. 151 (2020), Iss. P.494
https://doi.org/10.1016/j.apnum.2019.12.003 [Citations: 3]