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Sib. Zh. Vychisl. Mat., 2009, Volume 12, Number 1, Pages 1–15 (Mi sjvm1)  

This article is cited in 2 scientific papers (total in 2 papers)

The factorization method for linear and quasilinear singularly perturbed boundary problems for ordinary differential equations

A. F. Voevodin

M. A. Lavrent'ev Institute of Hydrodynamics

Abstract: For linear singularly perturbed boundary value problems we offer the method that reduces solving a differential problem to a discrete (difference) problem. The difference equations are constructed by the factorization method and are an exact analogy of differential equations. The coefficients of difference equations are calculated by solving the Cauchy problems for first order differential equations. In this case, the nonlinear Ricatti equations with a small parameter are solved by the asymptotic method, and linear equations are solved by the numerical methods. Solution to the quasilinear singularly perturbed equations is obtained by the implicit relaxation method. The solution to a linearized problem is calculated by analogy with a linear problem at each iterative steP. The method is tested with the known Lagestrome-Cole problem.

Key words: factorization method, asymptotic method, relaxation method.

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English version:
Numerical Analysis and Applications, 2009, 2:1, 1–12

UDC: 519.632.4
Received: 11.04.2008

Citation: A. F. Voevodin, “The factorization method for linear and quasilinear singularly perturbed boundary problems for ordinary differential equations”, Sib. Zh. Vychisl. Mat., 12:1 (2009), 1–15; Num. Anal. Appl., 2:1 (2009), 1–12

Citation in format AMSBIB
\Bibitem{Voe09}
\by A.~F.~Voevodin
\paper The factorization method for linear and quasilinear singularly perturbed boundary problems for ordinary differential equations
\jour Sib. Zh. Vychisl. Mat.
\yr 2009
\vol 12
\issue 1
\pages 1--15
\mathnet{http://mi.mathnet.ru/sjvm1}
\transl
\jour Num. Anal. Appl.
\yr 2009
\vol 2
\issue 1
\pages 1--12
\crossref{https://doi.org/10.1134/S1995423909010017}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-65249162294}


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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. A. F. Voevodin, “The method of conjugate operators for solving boundary value problems for ordinary second order differential equations”, Num. Anal. Appl., 5:3 (2012), 204–212  mathnet  crossref  elib
    2. A. V. Penenko, “Discrete-analytic schemes for solving an inverse coefficient heatconduction problem in a layered medium with gradient methods”, Num. Anal. Appl., 5:4 (2012), 326–341  mathnet  crossref  elib
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