This article is cited in 8 papers

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

I. A. Blatov^a, A. I. Zadorin^b, E. V. Kitaeva<sup>c

a</sup> Volga State University of Telecommunications and Informatics, Samara, Russia
^b Sobolev Institute of Mathematics, Omsk Branch, Omsk, Russia
^c Samara National Research University, Samara, Russia

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.

Keywords: boundary layer, large gradient, parabolic spline, Shishkin mesh, interpolation accuracy.

UDC: 519.652

MSC: 35R30

Received: 05.07.2016

DOI: 10.17377/smzh.2017.58.403

 English version: Siberian Mathematical Journal, 2017, 58:4, 578–590

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