Abstract
A subject of the article is a parabolic spline-interpolation of functions having high gradient domains. Uniform grids’ inefficiency was shown. The piecewise-uniform grids, concentrated in the boundary layer were scrutinized. There were announced asymptotically exact estimates on a class of functions with an exponential boundary layer in consideration with the traditional parabolic spline interpolation. There were obtained results showing non-uniform in small parameter estimates. A probable divergence of interpolation processes was extrapolated. A modified parabolic spline with obtained uniform in small parameter interpolation error estimations was introduced. The paper contains results of numerical experiments, which strengthen theoretical estimates.
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