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Volume 14, Issue 2
Efficient and Accurate Legendre Spectral Element Methods for One-Dimensional Higher Order Problems

Yang Zhang, Xuhong Yu & Zhongqing Wang

DOI: 10.4208/nmtma.OA-2020-0082

Numer. Math. Theor. Meth. Appl., 14 (2021), pp. 461-487.

Published online: 2021-01

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  • 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. 

  • Keywords

Legendre spectral element methods, higher order differential equations, Sobolev orthogonal/biorthogonal basis functions, high oscillatory or steep gradient solutions.

  • AMS Subject Headings

35G31, 35Q53, 65M70, 65N35, 33C45

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-14-461, author = {Zhang , YangYu , Xuhong and Wang , Zhongqing}, title = {Efficient and Accurate Legendre Spectral Element Methods for One-Dimensional Higher Order Problems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2021}, volume = {14}, number = {2}, pages = {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. 

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2020-0082}, url = {http://global-sci.org/intro/article_detail/nmtma/18607.html} }
TY - JOUR T1 - Efficient and Accurate Legendre Spectral Element Methods for One-Dimensional Higher Order Problems AU - Zhang , Yang AU - Yu , Xuhong AU - Wang , Zhongqing JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 461 EP - 487 PY - 2021 DA - 2021/01 SN - 14 DO - http://doi.org/10.4208/nmtma.OA-2020-0082 UR - https://global-sci.org/intro/article_detail/nmtma/18607.html KW - Legendre spectral element methods, higher order differential equations, Sobolev orthogonal/biorthogonal basis functions, high oscillatory or steep gradient solutions. AB -

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. 

Zhang , YangYu , Xuhong and Wang , Zhongqing. (2021). Efficient and Accurate Legendre Spectral Element Methods for One-Dimensional Higher Order Problems. Numerical Mathematics: Theory, Methods and Applications. 14 (2). 461-487. doi:10.4208/nmtma.OA-2020-0082
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