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Superconvergence of a Chebyshev Spectral Collocation Method

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Abstract

We reveal the relationship between a Petrov–Galerkin method and a spectral collocation method at the Chebyshev points of the second kind (±1 and zeros of U k ) for the two-point boundary value problem. Derivative superconvergence points are identified as the Chebyshev points of the first kind (Zeros of T k ). Super-geometric convergent rate is established for a special class of solutions.

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Authors and Affiliations

  1. College of Mathematics and Computer Science, Hunan Normal University, 410081, Changsha, China

    Zhimin Zhang

  2. Department of Mathematics, Wayne State University, 48202, Detroit, MI, USA

    Zhimin Zhang

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  1. Zhimin Zhang
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Correspondence to Zhimin Zhang.

Additional information

This work was supported in part by the US National Science Foundation grants DMS-0311807 and DMS-0612908.

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Zhang, Z. Superconvergence of a Chebyshev Spectral Collocation Method. J Sci Comput 34, 237–246 (2008). https://doi.org/10.1007/s10915-007-9163-7

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  • DOI: https://doi.org/10.1007/s10915-007-9163-7

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