Volume 12, Issue 1
Diagonalized Chebyshev Rational Spectral Methods for Second-Order Elliptic Problems on Unbounded Domains

Yanmin Ren, Xuhong Yu & Zhongqing Wang

Numer. Math. Theor. Meth. Appl., 12 (2019), pp. 265-284.

Published online: 2018-09

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  • Abstract

Diagonalized Chebyshev rational spectral methods for solving second-order elliptic problems on the half/whole line are proposed. Some Sobolev bi-orthogonal rational 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-like Chebyshev rational series. Numerical results demonstrate the effectiveness of the suggested approaches.

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@Article{NMTMA-12-265, author = {}, title = {Diagonalized Chebyshev Rational Spectral Methods for Second-Order Elliptic Problems on Unbounded Domains}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2018}, volume = {12}, number = {1}, pages = {265--284}, abstract = {

Diagonalized Chebyshev rational spectral methods for solving second-order elliptic problems on the half/whole line are proposed. Some Sobolev bi-orthogonal rational 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-like Chebyshev rational series. Numerical results demonstrate the effectiveness of the suggested approaches.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2018-0022}, url = {http://global-sci.org/intro/article_detail/nmtma/12700.html} }
TY - JOUR T1 - Diagonalized Chebyshev Rational Spectral Methods for Second-Order Elliptic Problems on Unbounded Domains JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 265 EP - 284 PY - 2018 DA - 2018/09 SN - 12 DO - http://doi.org/10.4208/nmtma.OA-2018-0022 UR - https://global-sci.org/intro/article_detail/nmtma/12700.html KW - AB -

Diagonalized Chebyshev rational spectral methods for solving second-order elliptic problems on the half/whole line are proposed. Some Sobolev bi-orthogonal rational 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-like Chebyshev rational series. Numerical results demonstrate the effectiveness of the suggested approaches.

Yanmin Ren, Xuhong Yu & Zhongqing Wang. (2020). Diagonalized Chebyshev Rational Spectral Methods for Second-Order Elliptic Problems on Unbounded Domains. Numerical Mathematics: Theory, Methods and Applications. 12 (1). 265-284. doi:10.4208/nmtma.OA-2018-0022
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