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Zh. Vychisl. Mat. Mat. Fiz., 2009, Volume 49, Number 3, Pages 518–541 (Mi zvmmf28)  

This article is cited in 4 scientific papers (total in 4 papers)

Numerical algorithm for solving diffusion equations on the basis of multigrid methods

M. E. Ladonkina, O. Yu. Milyukova, V. F. Tishkin

Institute for Mathematical Modeling, Russian Academy of Sciences, pl. Miusskaya 4a, Moscow, 125047, Russia

Abstract: A new effective algorithm based on multigrid methods is proposed for solving parabolic equations. The algorithm preserves implicit-scheme advantages (such as stability, accuracy, and conservativeness) while it involves a considerably reduced amount of arithmetic operations at every time level. The absolute stability, conservativeness, and convergence of the algorithm is proved theoretically using one- and two-dimensional initial-boundary value model problems for the heat equation. The error of the solution is estimated. The good accuracy of the method is demonstrated using two-dimensional model problems, including ones with discontinuous coefficients.

Key words: parabolic equations, multigrid methods, conservative scheme, stability and accuracy of a method.

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English version:
Computational Mathematics and Mathematical Physics, 2009, 49:3, 502–524

Bibliographic databases:

Document Type: Article
UDC: 519.634
Received: 10.07.2008

Citation: M. E. Ladonkina, O. Yu. Milyukova, V. F. Tishkin, “Numerical algorithm for solving diffusion equations on the basis of multigrid methods”, Zh. Vychisl. Mat. Mat. Fiz., 49:3 (2009), 518–541; Comput. Math. Math. Phys., 49:3 (2009), 502–524

Citation in format AMSBIB
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\paper Numerical algorithm for solving diffusion equations on the basis of multigrid methods
\jour Zh. Vychisl. Mat. Mat. Fiz.
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\vol 49
\issue 3
\pages 518--541
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\vol 49
\issue 3
\pages 502--524
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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. M. E. Ladonkina, O. Yu. Milyukova, V. F. Tishkin, “A numerical method for solving diffusion-type equations based on a multigrid method”, Comput. Math. Math. Phys., 50:8 (2010), 1367–1390  mathnet  crossref  mathscinet  adsnasa  isi
    2. O. Yu. Milyukova, V. F. Tishkin, “Chislennyi metod resheniya uravneniya teploprovodnosti na treugolnykh setkakh na osnove mnogosetochnogo metoda”, Preprinty IPM im. M. V. Keldysha, 2011, 029, 16 pp.  mathnet
    3. O. Yu. Milyukova, V. F. Tishkin, “Chislennyi metod resheniya uravneniya teploprovodnosti s razryvnym koeffitsientom na osnove mnogosetochnogo metoda”, Preprinty IPM im. M. V. Keldysha, 2013, 064, 19 pp.  mathnet
    4. M. V. Muratov, I. B. Petrov, I. E. Kvasov, “Chislennoe reshenie zadach seismorazvedki v zonakh treschinovatykh rezervuarov”, Matem. modelirovanie, 28:7 (2016), 31–44  mathnet  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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