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Generalized Jacobi Rational Spectral Method and Its Applications

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Abstract

We introduce an orthogonal system on the whole line, induced by the generalized Jacobi functions. Some results on the generalized Jacobi rational approximation are established, which play important roles in the related spectral methods. As examples of applications, the rational spectral schemes are proposed for sine-Gordon, Klein-Gordon and Fisher equations, with the convergence analysis. Numerical results demonstrate their efficiency.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Normal University, Scientific Computing Key Laboratory of Shanghai Universities, Division of Computational Science of E-institute of Shanghai Universities, Shanghai, 200234, China

    Ben-Yu Guo

  2. Department of Basic Courses, Tianhua College, Shanghai, 201805, China

    Yong-Gang Yi

Authors
  1. Ben-Yu Guo
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  2. Yong-Gang Yi
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Correspondence to Ben-Yu Guo.

Additional information

The work of B.-Y. Guo is supported in part by NSF of China N. 10871131, The Science and Technology Commission of Shanghai Municipality, Grant N. 075105118, Shanghai Leading Academic Discipline Project N. S30405 and Fund for E-institute of Shanghai Universities N. E03004.

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Guo, BY., Yi, YG. Generalized Jacobi Rational Spectral Method and Its Applications. J Sci Comput 43, 201–238 (2010). https://doi.org/10.1007/s10915-010-9353-6

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  • DOI: https://doi.org/10.1007/s10915-010-9353-6

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