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Generalized Jacobi Approximation in Multiple Dimensions and Its Applications

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Abstract

In this paper, we investigate the generalized Jacobi approximation in multiple dimensions. Some results on the generalized Jacobi orthogonal approximation and the generalized Jacobi-Gauss-Lobatto interpolation are established, which serve as useful tools in spectral and pseudospectral methods for differential equations of high order, whose coefficients might blow up or degenerate. As examples of applications, we provide the spectral schemes for two problems of fourth order, with Dirichlet boundary condition and mixed boundary condition respectively. Their spectral accuracy are proved. Efficient algorithms are implemented. Numerical results demonstrate the high accuracy of suggested algorithms.

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Acknowledgements

The work of this author is supported in part by NSF of China No. 11171227, and Fund for E-institute of Shanghai Universities No. E03004.

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Authors and Affiliations

  1. Dept. of Appl. Math., Shanghai Finance University, Shanghai, 201209, China

    Tao Sun

  2. Dept. of Math., Shanghai Normal University, Shanghai, 200234, China

    Ben-yu Guo

  3. Scientific Computing Key Laboratory of Shanghai University, Division of Computational Science of E-institute of Shanghai University, Shanghai University, Shanghai, China

    Ben-yu Guo

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  1. Tao Sun
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  2. Ben-yu Guo
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Correspondence to Ben-yu Guo.

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Sun, T., Guo, By. Generalized Jacobi Approximation in Multiple Dimensions and Its Applications. J Sci Comput 55, 327–350 (2013). https://doi.org/10.1007/s10915-012-9633-4

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  • DOI: https://doi.org/10.1007/s10915-012-9633-4

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