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    Convergence analysis of pseudospectral collocation methods for a singular differential equation

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    HuangW_SJoNA_41(6)2333.pdf (200.0Kb)
    Issue Date
    2003-01-02
    Author
    Huang, Weizhang
    Ma, Heping
    Sun, Weizwei
    Publisher
    Society for Industrial and Applied Mathematics
    Type
    Article
    Article Version
    Scholarly/refereed, publisher version
    Metadata
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    Abstract
    Solutions of partial differential equations with coordinate singularities often have special behavior near the singularities, which forces them to be smooth. Special treatment for these coordinate singularities is necessary in spectral approximations in order to avoid degradation of accuracy and efficiency. It has been observed numerically in the past that, for a scheme to attain high accuracy, it is unnecessary to impose all the pole conditions, the constraints representing the special solution behavior near singularities. In this paper we provide a theoretical justification for this observation. Specifically, we consider an existing approach, which uses a pole condition as the boundary condition at a singularity and solves the reformulated boundary value problem with a commonly used Gauss--Lobatto collocation scheme. Spectral convergence of the Legendre and Chebyshev collocation methods is obtained for a singular differential equation arising from polar and cylindrical geometries.
    Description
    This is the published version, also available here: http://dx.doi.org/10.1137/S0036142902381024.
    URI
    http://hdl.handle.net/1808/16874
    DOI
    https://doi.org/10.1137/S0036142902381024
    Collections
    • Mathematics Scholarly Works [282]
    Citation
    Huang, Weizhang., Ma, Heping., Sun, Weiwei. "Convergence analysis of pseudospectral collocation methods for a singular differential equation." SIAM J. Numer. Anal., 41(6), 2333–2349. (17 pages). http://dx.doi.org/10.1137/S0036142902381024.

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    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

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