Journal of Scientific Computing

, Volume 34, Issue 3, pp 237–246

Superconvergence of a Chebyshev Spectral Collocation Method

Article

DOI: 10.1007/s10915-007-9163-7

Cite this article as:
Zhang, Z. J Sci Comput (2008) 34: 237. doi:10.1007/s10915-007-9163-7

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 polynomialsCollocationSpectral methodSuperconvergencePetrov–Galerkin

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