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Matem. Mod., 2017, Volume 29, Number 12, Pages 16–28 (Mi mm3915)  

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

Compact difference scheme for the differential equation with piecewise-constant coefficient

V. A. Gordinab, E. A. Tsymbalovac

a National Research University Higher school of economics
b Hydrometeorological Center of Russia
c Skolkovo Institute of Science and Technology

Abstract: We present compact difference approximation on equidistant grid for the Dirichlet problem for the second order divergent type linear differential equation with piecewise-constant coefficient and discontinuous right hand side. Our numerical experiments demonstrate essential advantage of the scheme in comparison with the classic divergence scheme. We obtain same results for the Sturm–Liouville problem. The Richardson extrapolation method improves the order of accuracy in both cases.

Keywords: compact difference scheme, divergence difference scheme, stencil, discontinuous coefficient, double-sweep, order of convergence, Richardson extrapolation.

Funding Agency Grant Number
National Research University Higher School of Economics 16-05-0069
Ministry of Education and Science of the Russian Federation


Full text: PDF file (589 kB)
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Received: 17.10.2016

Citation: V. A. Gordin, E. A. Tsymbalov, “Compact difference scheme for the differential equation with piecewise-constant coefficient”, Matem. Mod., 29:12 (2017), 16–28

Citation in format AMSBIB
\Bibitem{GorTsy17}
\by V.~A.~Gordin, E.~A.~Tsymbalov
\paper Compact difference scheme for the differential equation with piecewise-constant coefficient
\jour Matem. Mod.
\yr 2017
\vol 29
\issue 12
\pages 16--28
\mathnet{http://mi.mathnet.ru/mm3915}
\elib{http://elibrary.ru/item.asp?id=30674649}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. A. Gordin, “Kompaktnye raznostnye skhemy dlya approksimatsii differentsialnykh sootnoshenii”, Matem. modelirovanie, 31:7 (2019), 58–74  mathnet  crossref  elib
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