On interpolation of functions with a boundary layer by parabolic splines

Abstract

A subject of the article is parabolic spline-interpolation of functions having high gradient domains. Uniform grids are proved inefficient. As for parabolic spline interpolation, asymptotically exact estimates on a class of functions with an exponential boundary layer are announced in regard with piecewise-uniform grids, concentrated in the boundary layer. There are obtained results showing non-uniform in small parameter estimates and divergence of interpolation processes. The author offered a modified parabolic spline for which uniform in small parameter interpolation error estimations were obtained. There are available results of numerical experiments confirming theoretical estimates.