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Sib. Zh. Ind. Mat., 2013, Volume 16, Number 1, Pages 42–55 (Mi sjim765)  

This article is cited in 3 scientific papers (total in 3 papers)

A two-grid method for a nonlinear singular perturbation boundary value problem on the Shishkin scheme

A. I. Zadorin, S. V. Tikhovskaya

Omsk Deaprtment of the Sobolev Institute of Mathematics of the SDRAS, Omsk, Russia

Abstract: Unders consideration is some boundary value problem for a second order nonlinear singular perturbation ordinary differential equationd. An upwind scheme on the Shishkin mesh is applied. We use the Newton and Picard methods to resolve the difference schemeare investigated. To decrease number of arithmetical operations we use the two-grid method. Application of the Richardson extrapolation is shown to give almost second order accuracy of the difference scheme. The results of some numerical experiments are discussed.

Keywords: nonlinear differential equation, singular perturbation, Shishkin mesh, difference scheme, iterative method, two-grid method, Richardson extrapolation.

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Bibliographic databases:
UDC: 519.62
Received: 01.02.2013

Citation: A. I. Zadorin, S. V. Tikhovskaya, “A two-grid method for a nonlinear singular perturbation boundary value problem on the Shishkin scheme”, Sib. Zh. Ind. Mat., 16:1 (2013), 42–55

Citation in format AMSBIB
\Bibitem{ZadTik13}
\by A.~I.~Zadorin, S.~V.~Tikhovskaya
\paper A two-grid method for a~nonlinear singular perturbation boundary value problem on the Shishkin scheme
\jour Sib. Zh. Ind. Mat.
\yr 2013
\vol 16
\issue 1
\pages 42--55
\mathnet{http://mi.mathnet.ru/sjim765}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3203304}


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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., Zadorin A.I., “a Two-Grid Method With Richardson Extrapolation For a Semilinear Convection-Diffusion Problem”, Application of Mathematics in Technical and Natural Sciences (AMITANS'15), AIP Conf. Proc., 1684, ed. Todorov M., Amer. Inst. Phys., 2015, 090007  crossref  mathscinet  isi  scopus
    2. S. V. Tikhovskaya, A. I. Zadorin, “Analysis of polynomial interpolation of the function of two variables with large gradients in the parabolic boundary layers”, Application of Mathematics in Technical and Natural Sciences (AMITANS'16), AIP Conf. Proc., 1773, ed. M. Todorov, Amer. Inst. Phys., 2016, 100008  crossref  isi
    3. S. V. Tikhovskaya, “Analysis of the numerical differentiation formulas of functions with large gradients”, Application of Mathematics in Technical and Natural Sciences, AIP Conf. Proc., 1895, ed. M. Todorov, Amer. Inst. Phys., 2017, UNSP 110010-1  crossref  isi  scopus
  • Сибирский журнал индустриальной математики
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