Journal of Scientific Computing

, Volume 34, Issue 3, pp 237–246

Superconvergence of a Chebyshev Spectral Collocation Method

Article

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 Uk) for the two-point boundary value problem. Derivative superconvergence points are identified as the Chebyshev points of the first kind (Zeros of Tk). Super-geometric convergent rate is established for a special class of solutions.

Keywords

Chebyshev polynomials Collocation Spectral method Superconvergence Petrov–Galerkin 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.College of Mathematics and Computer ScienceHunan Normal UniversityChangshaChina
  2. 2.Department of MathematicsWayne State UniversityDetroitUSA

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