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A fully diagonalized spectral method using generalized Laguerre functions on the half line

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Abstract

A fully diagonalized spectral method using generalized Laguerre functions is proposed and analyzed for solving elliptic equations on the half line. We first define the generalized Laguerre functions which are complete and mutually orthogonal with respect to an equivalent Sobolev inner product. Then the Fourier-like Sobolev orthogonal basis functions are constructed for the diagonalized Laguerre spectral method of elliptic equations. Besides, a unified orthogonal Laguerre projection is established for various elliptic equations. On the basis of this orthogonal Laguerre projection, we obtain optimal error estimates of the fully diagonalized Laguerre spectral method for both Dirichlet and Robin boundary value problems. Finally, numerical experiments, which are in agreement with the theoretical analysis, demonstrate the effectiveness and the spectral accuracy of our diagonalized method.

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Acknowledgments

The first author was supported by Science and Technology Research Program of Education Department of Henan Province (No. 13A110005); The second author was supported by National Natural Science Foundation of China (No. 11571238) and the Research Fund for Doctoral Program of Higher Education of China (No. 20133127110006); The third author was supported by National Natural Science Foundation of China (Nos. 91130014, 11471312 and 91430216).

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Authors and Affiliations

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

    Fu-Jun Liu & Zhong-Qing Wang

  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

Authors
  1. Fu-Jun Liu
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  2. Zhong-Qing Wang
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  3. Hui-Yuan Li
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Correspondence to Zhong-Qing Wang.

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Communicated by: Jan Hesthaven

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Liu, FJ., Wang, ZQ. & Li, HY. A fully diagonalized spectral method using generalized Laguerre functions on the half line. Adv Comput Math 43, 1227–1259 (2017). https://doi.org/10.1007/s10444-017-9522-3

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  • DOI: https://doi.org/10.1007/s10444-017-9522-3

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