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Matem. Mod., 2013, Volume 25, Number 11, Pages 53–64 (Mi mm3418)  

This article is cited in 5 scientific papers (total in 5 papers)

Error estimation for the diffusion equation solution based on the schemes with weights

A. I. Sukhinov, A. E. Chistyakov, A. V. Shishenya

Taganrog Institute of Technology of the South Federal University

Abstract: In applied problems it is often necessary to solve diffusion equation. The most efficient methods for solving such types of problems are grid methods that, nevertheless, have an approximation error. In the given paper a linear diffusion equation with variable coefficients is considered, for which estimation for error of approximation by scheme with weights is obtained. A method for the calculation of the optimal weight, which provides a minimum error for the given value of the grid spacing, is developed.

Keywords: diffusion equation; schemes with weights; approximation error.

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English version:
Mathematical Models and Computer Simulations, 2014, 6:3, 324–331

Bibliographic databases:

UDC: 519.6
Received: 18.06.2012

Citation: A. I. Sukhinov, A. E. Chistyakov, A. V. Shishenya, “Error estimation for the diffusion equation solution based on the schemes with weights”, Matem. Mod., 25:11 (2013), 53–64; Math. Models Comput. Simul., 6:3 (2014), 324–331

Citation in format AMSBIB
\Bibitem{SukChiShi13}
\by A.~I.~Sukhinov, A.~E.~Chistyakov, A.~V.~Shishenya
\paper Error estimation for the diffusion equation solution based on the schemes with weights
\jour Matem. Mod.
\yr 2013
\vol 25
\issue 11
\pages 53--64
\mathnet{http://mi.mathnet.ru/mm3418}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3220574}
\transl
\jour Math. Models Comput. Simul.
\yr 2014
\vol 6
\issue 3
\pages 324--331
\crossref{https://doi.org/10.1134/S2070048214030120}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84925937227}


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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. V. Nikitina, M. V. Puchkin, I. S. Semenov, A. I. Sukhinov, G. A. Ugolnitskii, A. B. Usov, A. E. Chistyakov, “Differentsialno-igrovaya model predotvrascheniya zamorov v melkovodnykh vodoemakh”, UBS, 55 (2015), 343–361  mathnet  elib
    2. A. I. Sukhinov, D. S. Khachunts, A. E. Chistyakov, “A mathematical model of pollutant propagation in near-ground atmospheric layer of a coastal region and its software implementation”, Comput. Math. Math. Phys., 55:7 (2015), 1216–1231  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    3. A. I. Sukhinov, A. E. Chistyakov, M. V. Yakobovskii, “Tochnost chislennogo resheniya uravneniya diffuzii-konvektsii na osnove raznostnykh skhem vtorogo i chetvertogo poryadkov pogreshnosti approksimatsii”, Vestn. YuUrGU. Ser. Vych. matem. inform., 5:1 (2016), 47–62  mathnet  crossref  elib
    4. A. I. Sukhinov, A. E. Chistyakov, A. A. Semenyakina, A. V. Nikitina, “Chislennoe modelirovanie ekologicheskogo sostoyaniya Azovskogo morya s primeneniem skhem povyshennogo poryadka tochnosti na mnogoprotsessornoi vychislitelnoi sisteme”, Kompyuternye issledovaniya i modelirovanie, 8:1 (2016), 151–168  mathnet  crossref
    5. A. I. Sukhinov, A. E. Chistyakov, “Error solving the wave equation based on the scheme with weights”, Math. Models Comput. Simul., 9:6 (2017), 649–656  mathnet  crossref  elib
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