Volume 13, Issue 2
Well-Conditioned Spectral Collocation Methods for Problems in Unbounded Domains

Dongqin Gu, Chao Zhang & Zhongqing Wang

Numer. Math. Theor. Meth. Appl., 13 (2020), pp. 452-478.

Published online: 2020-03

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  • Abstract

Based on the generalized Laguerre and Hermite functions, we construct two types of Birkhoff-type interpolation basis functions. The explicit expressions are derived, and fast and stable algorithms are provided for computing these basis functions. As applications, some well-conditioned collocation methods are proposed for solving various second-order differential equations in unbounded domains. Numerical experiments illustrate that our collocation methods are more efficient than the standard Laguerre/Hermite collocation approaches.

  • Keywords

Spectral collocation methods, generalized Laguerre and Hermite functions, Birkhoff interpolation, fast and stable algorithms.

  • AMS Subject Headings

65N35, 65M70, 33C45, 41A05, 41A30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

gudongqin1993@163.com (Dongqin Gu)

chaozhang@jsnu.edu.cn (Chao Zhang)

zqwang@usst.edu.cn (Zhongqing Wang)

  • BibTex
  • RIS
  • TXT
@Article{NMTMA-13-452, author = {Gu , Dongqin and Zhang , Chao and Wang , Zhongqing }, title = {Well-Conditioned Spectral Collocation Methods for Problems in Unbounded Domains}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2020}, volume = {13}, number = {2}, pages = {452--478}, abstract = {

Based on the generalized Laguerre and Hermite functions, we construct two types of Birkhoff-type interpolation basis functions. The explicit expressions are derived, and fast and stable algorithms are provided for computing these basis functions. As applications, some well-conditioned collocation methods are proposed for solving various second-order differential equations in unbounded domains. Numerical experiments illustrate that our collocation methods are more efficient than the standard Laguerre/Hermite collocation approaches.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2019-0090}, url = {http://global-sci.org/intro/article_detail/nmtma/15487.html} }
TY - JOUR T1 - Well-Conditioned Spectral Collocation Methods for Problems in Unbounded Domains AU - Gu , Dongqin AU - Zhang , Chao AU - Wang , Zhongqing JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 452 EP - 478 PY - 2020 DA - 2020/03 SN - 13 DO - http://doi.org/10.4208/nmtma.OA-2019-0090 UR - https://global-sci.org/intro/article_detail/nmtma/15487.html KW - Spectral collocation methods, generalized Laguerre and Hermite functions, Birkhoff interpolation, fast and stable algorithms. AB -

Based on the generalized Laguerre and Hermite functions, we construct two types of Birkhoff-type interpolation basis functions. The explicit expressions are derived, and fast and stable algorithms are provided for computing these basis functions. As applications, some well-conditioned collocation methods are proposed for solving various second-order differential equations in unbounded domains. Numerical experiments illustrate that our collocation methods are more efficient than the standard Laguerre/Hermite collocation approaches.

Dongqin Gu, Chao Zhang & Zhongqing Wang. (2020). Well-Conditioned Spectral Collocation Methods for Problems in Unbounded Domains. Numerical Mathematics: Theory, Methods and Applications. 13 (2). 452-478. doi:10.4208/nmtma.OA-2019-0090
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