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Sib. Zh. Vychisl. Mat., 2011, Volume 14, Number 1, Pages 47–57 (Mi sjvm425)  

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

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

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.

Full text: PDF file (221 kB)
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English version:
Numerical Analysis and Applications, 2011, 4:1, 36–45

UDC: 519.62
Received: 15.02.2010

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Tikhovskaya S.V., “Analysis of the Numerical Differentiation Formulas of Functions With Large Gradients”, Application of Mathematics in Technical and Natural Sciences, AIP Conference Proceedings, 1895, ed. Todorov M., Amer Inst Physics, 2017, UNSP 110010-1  crossref  isi  scopus
  • Sibirskii Zhurnal Vychislitel'noi Matematiki
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