Parabolic spline interpolation for functions with large gradient in the boundary layer


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Abstract

We consider the problem of Subbotin’s parabolic spline interpolation for functions with large gradient domains. In the case of the common piecewise uniform Shishkin’s mesh we obtain two-sided accuracy estimates for the class of functions with exponential boundary layer. The spline interpolation accuracy estimates are not uniform in a small parameter, while the error itself can grow unboundedly as the small parameter vanishes and the number N of nodes remains fixed. We include the results of some simulations.

About the authors

I. A. Blatov

Volga State University of Telecommunications and Informatics

Author for correspondence.
Email: blatow@mail.ru
Russian Federation, Samara

A. I. Zadorin

Sobolev Institute of Mathematics, Omsk Branch

Email: blatow@mail.ru
Russian Federation, Omsk

E. V. Kitaeva

Samara National Research University

Email: blatow@mail.ru
Russian Federation, Samara

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