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Volume 32, Issue 4
Spectral and Spectral Element Methods for High Order Problems with Mixed Boundary Conditions

Benyu Guo, Tao Sun & Chao Zhang

DOI: 10.4208/jcm.1403-m4373

J. Comp. Math., 32 (2014), pp. 392-411.

Published online: 2014-08

[An open-access article; the PDF is free to any online user.]

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  • Abstract

In this paper, we investigate numerical methods for high order differential equations. We propose new spectral and spectral element methods for high order problems with mixed inhomogeneous boundary conditions, and prove their spectral accuracy by using the recent results on the Jacobi quasi-orthogonal approximation. Numerical results demonstrate the high accuracy of suggested algorithm, which also works well even for oscillating solutions.

  • Keywords

Spectral and spectral element methods, High order problems with mixed inhomogeneous boundary conditions.

  • AMS Subject Headings

65L60, 65M70.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-32-392, author = {Benyu Guo, Tao Sun and Chao Zhang}, title = {Spectral and Spectral Element Methods for High Order Problems with Mixed Boundary Conditions}, journal = {Journal of Computational Mathematics}, year = {2014}, volume = {32}, number = {4}, pages = {392--411}, abstract = {

In this paper, we investigate numerical methods for high order differential equations. We propose new spectral and spectral element methods for high order problems with mixed inhomogeneous boundary conditions, and prove their spectral accuracy by using the recent results on the Jacobi quasi-orthogonal approximation. Numerical results demonstrate the high accuracy of suggested algorithm, which also works well even for oscillating solutions.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1403-m4373}, url = {http://global-sci.org/intro/article_detail/jcm/9894.html} }
TY - JOUR T1 - Spectral and Spectral Element Methods for High Order Problems with Mixed Boundary Conditions AU - Benyu Guo, Tao Sun & Chao Zhang JO - Journal of Computational Mathematics VL - 4 SP - 392 EP - 411 PY - 2014 DA - 2014/08 SN - 32 DO - http://doi.org/10.4208/jcm.1403-m4373 UR - https://global-sci.org/intro/article_detail/jcm/9894.html KW - Spectral and spectral element methods, High order problems with mixed inhomogeneous boundary conditions. AB -

In this paper, we investigate numerical methods for high order differential equations. We propose new spectral and spectral element methods for high order problems with mixed inhomogeneous boundary conditions, and prove their spectral accuracy by using the recent results on the Jacobi quasi-orthogonal approximation. Numerical results demonstrate the high accuracy of suggested algorithm, which also works well even for oscillating solutions.

Benyu Guo, Tao Sun and Chao Zhang. (2014). Spectral and Spectral Element Methods for High Order Problems with Mixed Boundary Conditions. Journal of Computational Mathematics. 32 (4). 392-411. doi:10.4208/jcm.1403-m4373
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