Non-polynomial interpolation of functions in the presence of a boundary layer

Abstract

The question of interpolation of a function of one variable with large gradients in the boundary layer region is investigated. The problem is that applying of polynomial interpolation formulas on a uniform grid to functions with large gradients can lead to unacceptable errors. We study the interpolation formulas with an arbitrarily number of interpolation nodes which are exact on the singular component. This component is responsible for the main growth of the function in the boundary layer and can be found based on asymptotic expansions. It is proved that error estimates don’t depend on the singular component and its derivatives. In the case of an exponential boundary layer these estimates don’t depend on a small parameter.