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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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  • https://www.mathnet.ru/eng/sjvm425
  • https://www.mathnet.ru/eng/sjvm/v14/i1/p47
    • This publication is cited in the following 3 articles:
    1. S V Tikhovskaya, “A Cascadic Multigrid Algorithm on the Shishkin Mesh for a Singularly Perturbed Elliptic Problem with regular layers”, J. Phys.: Conf. Ser., 2182:1 (2022), 012034  crossref
    2. S V Tikhovskaya, “A Cascadic Multigrid Algorithm on the Shishkin Mesh for a Singularly Perturbed Elliptic Problem”, J. Phys.: Conf. Ser., 1901:1 (2021), 012052  crossref
    3. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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