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Matem. Mod., 2007, Volume 19, Number 4, Pages 71–89 (Mi mm949)  

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

Numerical algorithm for equations of diffusion type on base of multigrid methods

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

Institute for Mathematical Modelling, Russian Academy of Sciences

Abstract: The new efficient algorithm for solving of parabolic type equations on base of multigrid method is pro-posed, which conserves the advantages of implicit scheme – stability and accuracy, but permits essentially reduce the number of arithmetical operations on each time level. The absolute stability of proposed method is proved on example of one dimensional model problem, the approximation error is investigated and the estimate of solution error is obtained. The calculations of D and 2D model problems showed the good accuracy of proposed method.

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Received: 21.03.2006

Citation: M. E. Ladonkina, O. Yu. Milyukova, V. F. Tishkin, “Numerical algorithm for equations of diffusion type on base of multigrid methods”, Matem. Mod., 19:4 (2007), 71–89

Citation in format AMSBIB
\Bibitem{LadMilTis07}
\by M.~E.~Ladonkina, O.~Yu.~Milyukova, V.~F.~Tishkin
\paper Numerical algorithm for equations of diffusion type on base of multigrid methods
\jour Matem. Mod.
\yr 2007
\vol 19
\issue 4
\pages 71--89
\mathnet{http://mi.mathnet.ru/mm949}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2341637}
\zmath{https://zbmath.org/?q=an:1119.35337}


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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. M. E. Ladonkina, O. Yu. Milyukova, V. F. Tishkin, “Numerical algorithm for solving diffusion equations on the basis of multigrid methods”, Comput. Math. Math. Phys., 49:3 (2009), 502–524  mathnet  crossref  mathscinet  isi
    2. 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
    3. 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
    4. 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
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