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Sibirsk. Mat. Zh., 2017, Volume 58, Number 4, Pages 745–760 (Mi smj2894)  

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

I. A. Blatova, A. I. Zadorinb, E. V. Kitaevac

a 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.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-06584-а
16-01-00727-а
The authors were supported by the Russian Foundation for Basic Research (Grants 15-01-06584-a and 16-01-00727-a).


DOI: https://doi.org/10.17377/smzh.2017.58.403

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

Bibliographic databases:

UDC: 519.652
MSC: 35R30
Received: 05.07.2016

Citation: I. A. Blatov, A. I. Zadorin, E. V. Kitaeva, “Parabolic spline interpolation for functions with large gradient in the boundary layer”, Sibirsk. Mat. Zh., 58:4 (2017), 745–760; Siberian Math. J., 58:4 (2017), 578–590

Citation in format AMSBIB
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