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Sib. Zh. Vychisl. Mat., 2013, Volume 16, Number 1, Pages 11–25 (Mi sjvm494)  

This article is cited in 4 scientific papers (total in 4 papers)

Solution of second order nonlinear singular perturbation ordinary differential equation based on the Samarskii scheme

A. I. Zadorin, S. V. Tikhovskaya

Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Omsk

Abstract: A boundary value problem for a second order nonlinear singular perturbation ordinary differential equation is considered. We propose the method based on the Newton and the Picard linearizations using known modified Samarskii scheme on the Shishkin mesh in the case of a linear problem. It is proved that the constructed difference schemes are of second order and uniformly convergent. To decrease the number of the arithmetical operations, we propose a two-grid method. The results of some numerical experiments are discussed.

Key words: second order nonlinear ordinary differential equation, singular perturbation, Newton method, Picard method, Samarskii scheme, Shishkin mesh, uniform convergence, two-grid algorithm.

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English version:
Numerical Analysis and Applications, 2013, 6:1, 9–23

Bibliographic databases:

UDC: 519.62
Received: 09.11.2011

Citation: A. I. Zadorin, S. V. Tikhovskaya, “Solution of second order nonlinear singular perturbation ordinary differential equation based on the Samarskii scheme”, Sib. Zh. Vychisl. Mat., 16:1 (2013), 11–25; Num. Anal. Appl., 6:1 (2013), 9–23

Citation in format AMSBIB
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\paper Solution of second order nonlinear singular perturbation ordinary differential equation based on the Samarskii scheme
\jour Sib. Zh. Vychisl. Mat.
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\vol 16
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\pages 11--25
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3380103}
\elib{https://elibrary.ru/item.asp?id=20432478}
\transl
\jour Num. Anal. Appl.
\yr 2013
\vol 6
\issue 1
\pages 9--23
\crossref{https://doi.org/10.1134/S1995423913010023}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84874791754}


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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  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
    4. Tikhovskaya S.V., Korbut M.F., Xii International Scientific and Technical Conference Applied Mechanics and Systems Dynamics, Journal of Physics Conference Series, 1210, IOP Publishing Ltd, 2019  crossref  isi  scopus
  • Sibirskii Zhurnal Vychislitel'noi Matematiki
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