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The Chebyshev points are commonly used for spectral differentiation innon-periodic domains. The rounding error in the Chebyshev approximation to the$n$-the derivative increases at a rate greater than $n^{2m}$ for the $m$-thderivative. The mapping technique of Kosloff and Tal-Ezer (\emph{J. Comp.Physics}, vol. 104 (1993), p. 457-469) ameliorates this increase in roundingerror. We show that the argument used to justify the choice of the mappingparameter is substantially incomplete. We analyze rounding error as well asdiscretization error and give a more complete argument for the choice of themapping parameter. If the discrete cosine transform is used to computederivatives, we show that a different choice of the mapping parameter yieldsgreater accuracy.

Error Analysis of Finite Differences and the Mapping Parameter in Spectral Differentiation