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Matematicheskoe modelirovanie, 2016, Volume 28, Number 7, Pages 121–136 (Mi mm3753)  
This article is cited in 7 scientific papers (total in 7 papers)

Exponential difference schemes for solution of boundary problems for diffusion-convection equations

S. V. Polyakovab, Yu. N. Karamzina, T. A. Kudryashovaa, I. V. Tsybulinc

a Keldysh Institute of Applied Mathematics, Russian Academy of Scinces, 125047, Russia, Moscow, Miusskaya square, 4
b National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), 115409, Russia, Moscow, Kashirskoe highway, 31
c Moscow Institute of Physics and Technology, 141700, Moscow region, Dolgoprudny, Institutskiy lane, 9
Full-text PDF (427 kB) Citations (7)
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Abstract: The numerical solution of boundary-value problems is considered for multidimensional equations of convection-diffusion (CDE). These equations are used for many physical processes in solids, liquids and gases. A new approach to the spatial approximation for such equations is proposed. This approach is based on a integral transformation of second order differential operators. A linear version of CDE was selected to simplify analysis. For this variant, a new exponential difference schemes were offered, algorithms of its implementation were developed, a brief analysis of the stability and convergence was fulfilled. Numerical testing of approach was executed for a two-dimensional problem of metallic particles motion in the water flow under influence of a constant magnetic field.
Keywords: Convection-Diffusion Equation (CDE), Integral Transformation, Finite-Difference Schemes, Iterations, Non-monotonic sweep procedure.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 14.964.11.0001
Received: 01.03.2016
English version:
Mathematical Models and Computer Simulations, 2017, Volume 9, Issue 1, Pages 71–82
DOI: https://doi.org/10.1134/S2070048217010124
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: S. V. Polyakov, Yu. N. Karamzin, T. A. Kudryashova, I. V. Tsybulin, “Exponential difference schemes for solution of boundary problems for diffusion-convection equations”, Mat. Model., 28:7 (2016), 121–136; Math. Models Comput. Simul., 9:1 (2017), 71–82
Citation in format AMSBIB
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\by S.~V.~Polyakov, Yu.~N.~Karamzin, T.~A.~Kudryashova, I.~V.~Tsybulin
\paper Exponential difference schemes for solution of boundary problems for diffusion-convection equations
\jour Mat. Model.
\yr 2016
\vol 28
\issue 7
\pages 121--136
\mathnet{http://mi.mathnet.ru/mm3753}
\elib{https://elibrary.ru/item.asp?id=26604121}
\transl
\jour Math. Models Comput. Simul.
\yr 2017
\vol 9
\issue 1
\pages 71--82
\crossref{https://doi.org/10.1134/S2070048217010124}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85012005453}
Linking options:
  • https://www.mathnet.ru/eng/mm3753
  • https://www.mathnet.ru/eng/mm/v28/i7/p121
    • This publication is cited in the following 7 articles:
    1. Miglena N. Koleva, Lubin G. Vulkov, “Numerical Solution of External Boundary Conditions Inverse Multilayer Diffusion Problems”, Symmetry, 16:10 (2024), 1396  crossref
    2. Miglena N. Koleva, Sergey V. Polyakov, Lubin G. Vulkov, Studies in Computational Intelligence, 1111, Advanced Computing in Industrial Mathematics, 2023, 112  crossref
    3. T. P. Chernogorova, M. N. Koleva, L. G. Vulkov, “Exponential finite difference scheme for transport equations with discontinuous coefficients in porous media”, Appl. Math. Comput., 392 (2021), 125691  crossref  mathscinet  zmath  isi  scopus
    4. Sergey Polyakov, Tatiana Kudryashova, Nikita Tarasov, EngOpt 2018 Proceedings of the 6th International Conference on Engineering Optimization, 2019, 754  crossref
    5. Yury N. Karamzin, Tatiana A. Kudryashova, Sergey V. Polyakov, Viktoriia O. Podryga, Lecture Notes in Computer Science, 11386, Finite Difference Methods. Theory and Applications, 2019, 321  crossref
    6. Tatiana Kudryashova', Sergey Polyakov, Nikita Tarasov, N. Mastorakis, V. Mladenov, A. Bulucea, “A novel parallel algorithm for 3D modelling electromagnetic purification of water”, MATEC Web Conf., 210 (2018), 04027  crossref
    7. S. V. Polyakov, Yu. N. Karamzin, T. A. Kudryasova, N. I. Tarasov, “Mathematical modelling of water treatment processes”, Math. Montisnigri, 40 (2017), 110–126  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математическое моделирование
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    References:86
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