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Matem. Mod., 2017, Volume 29, Number 7, Pages 3–14 (Mi mm3863)  

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

4$^{\mathrm{th}}$ order difference scheme for the differential equation with variable coefficients

V. A. Gordinab, E. A. Tsymbalovbc

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

Abstract: We present compact difference scheme on three-point stencil for unknown function. The scheme approximates linear second order differential equation with variable smooth coefficient. Our numerical experiments confirmed 4-th accuracy order of solutions of the difference scheme and of eigenvalues approximation for the boundary problem. The difference operator is almost self-conjugate, and its spectrum is real. The Richardson extrapolation method improves the accuracy order.

Keywords: compact difference scheme, divergent scheme, test functions, self-conjugacy.

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


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English version:
Mathematical Models and Computer Simulations, 2018, 10:1, 79–88

Received: 10.10.2016

Citation: V. A. Gordin, E. A. Tsymbalov, “4$^{\mathrm{th}}$ order difference scheme for the differential equation with variable coefficients”, Matem. Mod., 29:7 (2017), 3–14; Math. Models Comput. Simul., 10:1 (2018), 79–88

Citation in format AMSBIB
\Bibitem{GorTsy17}
\by V.~A.~Gordin, E.~A.~Tsymbalov
\paper 4$^{\mathrm{th}}$ order difference scheme for the differential equation with variable coefficients
\jour Matem. Mod.
\yr 2017
\vol 29
\issue 7
\pages 3--14
\mathnet{http://mi.mathnet.ru/mm3863}
\elib{http://elibrary.ru/item.asp?id=29404328}
\transl
\jour Math. Models Comput. Simul.
\yr 2018
\vol 10
\issue 1
\pages 79--88
\crossref{https://doi.org/10.1134/S2070048218010064}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85042557369}


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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, E. A. Tsymbalov, “Kompaktnaya raznostnaya skhema dlya differentsialnogo uravneniya s kusochno-postoyannym koeffitsientom”, Matem. modelirovanie, 29:12 (2017), 16–28  mathnet  elib
    2. V. A. Gordin, E. A. Tsymbalov, “Compact difference scheme for parabolic and Schrödinger-type equations with variable coefficients”, J. Comput. Phys., 375 (2018), 1451–1468  crossref  mathscinet  isi  scopus
    3. V. A. Gordin, “Kompaktnye raznostnye skhemy dlya approksimatsii differentsialnykh sootnoshenii”, Matem. modelirovanie, 31:7 (2019), 58–74  mathnet  crossref  elib
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