Mappings and accuracy for Chebyshev pseudo-spectral approximations

The effect of mappings on the approximation, by Chebyshev collocation, of functions which exhibit localized regions of rapid variation is studied. A general strategy is introduced whereby mappings are adaptively constructed which map specified classes of rapidly varying functions into low order polynomials. A particular family of mappings constructed in this way is tested on a variety of rapidly varying functions similar to those occurring in applications. It is shown that the mapped function can be approximated much more accurately by Chebyshev polynomial approximations than the original function. The effect on the approximation of introducing subdomains is also studied. The accuracy of the pseudo-spectral approximation is very sensitive to the location of the interface, although this sensitivity is reduced when mappings are employed within the subdomains.