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Spectral methods using generalized Laguerre functions for second and fourth order problems

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Abstract

Spectral methods using generalized Laguerre functions are proposed for second-order equations under polar (resp. spherical) coordinates in ℝ2 (resp. ℝ3) and fourth-order equations on the half line. Some Fourier-like Sobolev orthogonal basis functions are constructed for our Laguerre spectral methods for elliptic problems. Optimal error estimates of the Laguerre spectral methods are obtained for both second-order and fourth-order elliptic equations. Numerical experiments demonstrate the effectiveness and the spectral accuracy.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China

    Fu-jun Liu

  2. School of Science, Henan Institute of Engineering, Zhengzhou, 451191, China

    Fu-jun Liu

  3. State Key Laboratory of Computer Science/Laboratory of Parallel Computing, Institute of Software, Chinese Academy of Sciences, Beijing, 100190, China

    Hui-yuan Li

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

    Zhong-qing Wang

Authors
  1. Fu-jun Liu
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  2. Hui-yuan Li
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  3. Zhong-qing Wang
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Correspondence to Hui-yuan Li.

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Liu, Fj., Li, Hy. & Wang, Zq. Spectral methods using generalized Laguerre functions for second and fourth order problems. Numer Algor 75, 1005–1040 (2017). https://doi.org/10.1007/s11075-016-0228-2

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  • DOI: https://doi.org/10.1007/s11075-016-0228-2

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