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Sib. Zh. Vychisl. Mat., 2017, Volume 20, Number 2, Pages 131–144 (Mi sjvm641)  

This article is cited in 1 scientific paper (total in 1 paper)

About the uniform convergence of parabolic spline interpolation on the class of functions with large gradients in the boundary layer

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

a Volga region state university of telecommunications and informatics, Moskovskoe shosse, 77, Samara, 443090, Russia
b Sobolev Institute of Mathematics, 4 Acad. Koptyug avenue, Novosibirsk, 630090, Russia
c Samara national research University named after academician S.P.  Korolyov, Moskovskoe shosse, 34, Samara, 443086, Russia

Abstract: A problem of the Subbotin parabolic spline-interpolation of functions with large gradients in the boundary layer is considered. In the case of a uniform grid it has been proved and in the case of the Shishkin grid it has been experimentally shown that with a parabolic spline-interpolation of functions with large gradients the error in the exponential boundary layer can unrestrictedly increase with a fixed number of grid nodes. A modified parabolic spline has been constructed. Estimates of the interpolation error of the constructed spline don't depend from a small parameter.

Key words: singular perturbation, boundary layer, Shishkin mesh, parabolic spline, modification, estimation of error.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-06584
16-01-00727


DOI: https://doi.org/10.15372/SJNM20170202

Full text: PDF file (597 kB)
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English version:
Numerical Analysis and Applications, 2017, 10:2, 108–119

Bibliographic databases:

UDC: 519.652
Received: 27.06.2016
Revised: 08.11.2016

Citation: I. A. Blatov, A. I. Zadorin, E. V. Kitaeva, “About the uniform convergence of parabolic spline interpolation on the class of functions with large gradients in the boundary layer”, Sib. Zh. Vychisl. Mat., 20:2 (2017), 131–144; Num. Anal. Appl., 10:2 (2017), 108–119

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. A. Blatov, A. I. Zadorin, E. V. Kitaeva, “An application of the cubic spline on Shishkin mesh for the approximation of a function and its derivatives in the presence of a boundary layer”, XII International Scientific and Technical Conference Applied Mechanics and Systems Dynamics, Journal of Physics Conference Series, 1210, IOP Publishing Ltd, 2019, 012017  crossref  isi  scopus
  • Sibirskii Zhurnal Vychislitel'noi Matematiki
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