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Orthogonal Jacobi Rational Functions and Spectral Methods on the Half Line

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Abstract

We introduce a new system of Jacobi rational functions, which is mutually orthogonal with respect to the weight function \(x^\beta \) on the half line. Some properties and approximation results on Jacobi rational functions are established. The Jacobi rational spectral methods are proposed for various elliptic boundary value problems on unbounded domains and their convergence is proved. Numerical results demonstrate the spectral accuracy of these approaches.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou, Jiangsu, 221111, China

    Dong-qin Gu

  2. School of Science, University of Shanghai for Science and Technology, Shanghai, 200093, China

    Dong-qin Gu & Zhong-qing Wang

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  1. Dong-qin Gu
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  2. Zhong-qing Wang
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Correspondence to Zhong-qing Wang.

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This work is supported by National Natural Science Foundation of China (No. 12071294).

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Gu, Dq., Wang, Zq. Orthogonal Jacobi Rational Functions and Spectral Methods on the Half Line. J Sci Comput 88, 17 (2021). https://doi.org/10.1007/s10915-021-01535-7

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  • DOI: https://doi.org/10.1007/s10915-021-01535-7

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