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