Sibirskii Zhurnal Vychislitel'noi Matematiki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Sib. Zh. Vychisl. Mat.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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
Full-text PDF (597 kB) Citations (6)
References:
PDF
HTML
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
\Bibitem{BlaZadKit17}
\by I.~A.~Blatov, A.~I.~Zadorin, E.~V.~Kitaeva
\paper About the uniform convergence of parabolic spline interpolation on the class of functions with large gradients in the boundary layer
\jour Sib. Zh. Vychisl. Mat.
\yr 2017
\vol 20
\issue 2
\pages 131--144
\mathnet{http://mi.mathnet.ru/sjvm641}
\crossref{https://doi.org/10.15372/SJNM20170202}
\elib{https://elibrary.ru/item.asp?id=29160406}
\transl
\jour Num. Anal. Appl.
\yr 2017
\vol 10
\issue 2
\pages 108--119
\crossref{https://doi.org/10.1134/S1995423917020021}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000405833000002}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85020172952}
Linking options:
  • https://www.mathnet.ru/eng/sjvm641
  • https://www.mathnet.ru/eng/sjvm/v20/i2/p131
    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Sibirskii Zhurnal Vychislitel'noi Matematiki
    Statistics & downloads:
    Abstract page:269
    Full-text PDF :44
    References:53
    First page:15
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024