The Accuracy of the Chebyshev Differencing Method for Analytic Functions

2005/01/01 by S. C. Reddy, S C Reddy, J. A. C. Weideman · 1 citation
Mathematics · Decision Sciences · Computer Science · #Numerical methods for differential equations #Probabilistic and Robust Engineering Design #Matrix Theory and Algorithms

paper · doi:10.1137/040603280

Abstract

The Chebyshev spectral collocation method is one of the most powerful tools for numerical differentiation, particularly when the function under consideration is smooth. An upper bound on the error, in the discrete maximum norm, is derived here when the function is analytic. Two model functions are analyzed in detail.

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