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Volume 16, Issue 2
New Rational Interpolation Basis Functions on the Unbounded Intervals and Their Applications

Dong-Qin Gu, Zhong-Qing Wang & Chao Zhang

DOI: 10.4208/nmtma.OA-2022-0109

Numer. Math. Theor. Meth. Appl., 16 (2023), pp. 453-488.

Published online: 2023-04

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  • Abstract

Based on the rational system of Legendre rational functions, we construct two set of new interpolation basis functions on the unbounded intervals. Their explicit expressions are derived, and fast and stable algorithms are provided for computing the new basis functions. As applications, new rational collocation methods based on these new basis functions are proposed for solving various second-order differential equations on the unbounded domains. Numerical experiments illustrate that our new methods are more effective and stable than the existing collocation methods.

  • Keywords

Rational collocation methods, Birkhoff interpolation, fast and stable algorithms.

  • AMS Subject Headings

65M70, 33C45, 30C15, 65N35, 41A05

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{NMTMA-16-453, author = {Gu , Dong-QinWang , Zhong-Qing and Zhang , Chao}, title = {New Rational Interpolation Basis Functions on the Unbounded Intervals and Their Applications}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2023}, volume = {16}, number = {2}, pages = {453--488}, abstract = {

Based on the rational system of Legendre rational functions, we construct two set of new interpolation basis functions on the unbounded intervals. Their explicit expressions are derived, and fast and stable algorithms are provided for computing the new basis functions. As applications, new rational collocation methods based on these new basis functions are proposed for solving various second-order differential equations on the unbounded domains. Numerical experiments illustrate that our new methods are more effective and stable than the existing collocation methods.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2022-0109}, url = {http://global-sci.org/intro/article_detail/nmtma/21585.html} }
TY - JOUR T1 - New Rational Interpolation Basis Functions on the Unbounded Intervals and Their Applications AU - Gu , Dong-Qin AU - Wang , Zhong-Qing AU - Zhang , Chao JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 453 EP - 488 PY - 2023 DA - 2023/04 SN - 16 DO - http://doi.org/10.4208/nmtma.OA-2022-0109 UR - https://global-sci.org/intro/article_detail/nmtma/21585.html KW - Rational collocation methods, Birkhoff interpolation, fast and stable algorithms. AB -

Based on the rational system of Legendre rational functions, we construct two set of new interpolation basis functions on the unbounded intervals. Their explicit expressions are derived, and fast and stable algorithms are provided for computing the new basis functions. As applications, new rational collocation methods based on these new basis functions are proposed for solving various second-order differential equations on the unbounded domains. Numerical experiments illustrate that our new methods are more effective and stable than the existing collocation methods.

Gu , Dong-QinWang , Zhong-Qing and Zhang , Chao. (2023). New Rational Interpolation Basis Functions on the Unbounded Intervals and Their Applications. Numerical Mathematics: Theory, Methods and Applications. 16 (2). 453-488. doi:10.4208/nmtma.OA-2022-0109
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