Year: 2021
Author: Yang Zhang, Zhongqing Wang, Xuhong Yu, Zhongqing Wang
Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 2 : pp. 461–487
Abstract
Efficient and accurate Legendre spectral element methods for solving one-dimensional higher order differential equations with high oscillatory or steep gradient solutions are proposed. Some Sobolev orthogonal/biorthogonal basis functions corresponding to each subinterval are constructed, which reduce the non-zero entries of linear systems and computational cost. Numerical experiments exhibit the effectiveness and accuracy of the suggested approaches.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2020-0082
Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 2 : pp. 461–487
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Legendre spectral element methods higher order differential equations Sobolev orthogonal/biorthogonal basis functions high oscillatory or steep gradient solutions.
Author Details
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Efficient spectral and spectral element methods for Sobolev equation with diagonalization technique
Yu, Xuhong
Wang, Mengyao
Applied Numerical Mathematics, Vol. 201 (2024), Iss. P.265
https://doi.org/10.1016/j.apnum.2024.03.008 [Citations: 0]