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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2017, Volume 20, Number 2, Pages 131–144
DOI: https://doi.org/10.15372/SJNM20170202 (Mi sjvm641) 		 
This article is cited in 6 scientific papers (total in 6 papers)

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
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DOI: https://doi.org/10.15372/SJNM20170202
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
Received: 27.06.2016
Revised: 08.11.2016
English version:
Numerical Analysis and Applications, 2017, Volume 10, Issue 2, Pages 108–119
DOI: https://doi.org/10.1134/S1995423917020021
Bibliographic databases:
Document Type: Article
UDC: 519.652
Language: Russian
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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    • This publication is cited in the following 6 articles:
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