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Matematicheskoe modelirovanie, 2017, Volume 29, Number 7, Pages 3–14 (Mi mm3863)  
This article is cited in 5 scientific papers (total in 5 papers)

4th 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
Full-text PDF (440 kB) Citations (5)
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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
Received: 10.10.2016
English version:
Mathematical Models and Computer Simulations, 2018, Volume 10, Issue 1, Pages 79–88
DOI: https://doi.org/10.1134/S2070048218010064
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. A. Gordin, E. A. Tsymbalov, “4th order difference scheme for the differential equation with variable coefficients”, Mat. Model., 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 Mat. Model.
\yr 2017
\vol 29
\issue 7
\pages 3--14
\mathnet{http://mi.mathnet.ru/mm3863}
\elib{https://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{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85042557369}
Linking options:
  • https://www.mathnet.ru/eng/mm3863
  • https://www.mathnet.ru/eng/mm/v29/i7/p3
    • This publication is cited in the following 5 articles:
    1. Liling Shen, “Parallel Solving Method for the Variable Coefficient Nonlinear Equation”, International Journal of Circuits, Systems and Signal Processing, 16 (2022), 264  crossref
    2. V. A. Gordin, “Compact finite-difference scheme for differential relations' approximation”, Math. Models Comput. Simul., 12:2 (2020), 133–142  mathnet  crossref  crossref  elib
    3. V.A. Gordin, “COMPACT FINITE-DIFFERENCE SCHEMES FOR WEAKLY NON-LINEAR PROBLEMS AND BOUNDARY CONDITIONS IMITATING CAUCHY PROBLEM”, JOR, 47:1 (2019), 32  crossref
    4. 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  zmath  adsnasa  isi  scopus
    5. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математическое моделирование
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