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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2011, Volume 14, Number 1, Pages 47–57 (Mi sjvm425)  
This article is cited in 3 scientific papers (total in 3 papers)

Analysis of a difference scheme for a singular perturbation Cauchy problem on refined grids

A. I. Zadorin, S. V. Tikhovskaya

Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Science, Omsk
Full-text PDF (221 kB) Citations (3)
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Abstract: A Cauchy problem for a singular perturbation second-order ordinary differential equation is considered. It is proved that the upwind difference scheme on a grid proposed by Shishkin is uniformly convergent. The grid is well known only in application to a boundary value problem. The results of some numerical experiments are discussed.
Key words: second order ordinary differential equation, singular perturbation, Cauchy problem, difference scheme, maximum principle, Shishkin mesh, uniform convergence.
Received: 15.02.2010
English version:
Numerical Analysis and Applications, 2011, Volume 4, Issue 1, Pages 36–45
DOI: https://doi.org/10.1134/S1995423911010046
Bibliographic databases:
Document Type: Article
UDC: 519.62
Language: Russian
Citation: A. I. Zadorin, S. V. Tikhovskaya, “Analysis of a difference scheme for a singular perturbation Cauchy problem on refined grids”, Sib. Zh. Vychisl. Mat., 14:1 (2011), 47–57; Num. Anal. Appl., 4:1 (2011), 36–45
Citation in format AMSBIB
\Bibitem{ZadTik11}
\by A.~I.~Zadorin, S.~V.~Tikhovskaya
\paper Analysis of a~difference scheme for a~singular perturbation Cauchy problem on refined grids
\jour Sib. Zh. Vychisl. Mat.
\yr 2011
\vol 14
\issue 1
\pages 47--57
\mathnet{http://mi.mathnet.ru/sjvm425}
\transl
\jour Num. Anal. Appl.
\yr 2011
\vol 4
\issue 1
\pages 36--45
\crossref{https://doi.org/10.1134/S1995423911010046}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79952467612}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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