Spline interpolation of functions with a boundary layer component (Q2896266)

The article is concerned with an interpolation technique for functions on a compact interval which have boundary layers, like e.g. solutions of singularly perturbed two-point boundary value problems, which involve exponential layers. To overcome the obvious difficulties with polynomial interpolation, an adapted spline interpolation technique is proposed which exploits knowledge about the singular (boundary layer) part. Corresponding error estimates are proved, and numerical examples are presented for illustration.