, Volume 34, Issue 3, pp 237-246
Date: 16 Oct 2007

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.

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