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Volume 15, Issue 1-2
Fully Diagonalized Chebyshev Spectral Methods for Second and Fourth Order Elliptic Boundary Value Problems

Jing-Min Li, Zhong-Qing Wang & Huiyuan Li

Int. J. Numer. Anal. Mod., 15 (2018), pp. 243-259.

Published online: 2018-01

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  • 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.

  • Keywords

Spectral method, biorthogonal Chebyshev polynomials, elliptic boundary value problems, numerical results.

  • AMS Subject Headings

76M22, 33C45, 35J40

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

ljm_destiny@163.com (Jing-Min Li)

zqwang@usst.edu. cn (Zhong-Qing Wang)

huiyuan@iscas.ac.cn (Huiyuan Li)

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-15-243, author = {Li , Jing-MinWang , Zhong-Qing and Li , Huiyuan}, title = {Fully Diagonalized Chebyshev Spectral Methods for Second and Fourth Order Elliptic Boundary Value Problems}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2018}, volume = {15}, number = {1-2}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/10566.html} }
TY - JOUR T1 - Fully Diagonalized Chebyshev Spectral Methods for Second and Fourth Order Elliptic Boundary Value Problems AU - Li , Jing-Min AU - Wang , Zhong-Qing AU - Li , Huiyuan JO - International Journal of Numerical Analysis and Modeling VL - 1-2 SP - 243 EP - 259 PY - 2018 DA - 2018/01 SN - 15 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/10566.html KW - Spectral method, biorthogonal Chebyshev polynomials, elliptic boundary value problems, numerical results. AB -

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.

Li , Jing-MinWang , Zhong-Qing and Li , Huiyuan. (2018). Fully Diagonalized Chebyshev Spectral Methods for Second and Fourth Order Elliptic Boundary Value Problems. International Journal of Numerical Analysis and Modeling. 15 (1-2). 243-259. doi:
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