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Trudy Inst. Mat. i Mekh. UrO RAN, 2010, Volume 16, Number 1, Pages 102–118 (Mi timm531)  

This article is cited in 3 scientific papers (total in 3 papers)

Convergence of the alternating direction method for the numerical solution of a heat conduction equation with delay

A. V. Lekomtsev, V. G. Pimenov

Ural State University

Abstract: Two-dimensional parabolic equations with delay effects in the time component are considered. An alternating direction scheme is constructed for the numerical solution of these equations. The question on the reduction of the problem with inhomogeneous boundary conditions to a problem with homogeneous boundary conditions is considered. The order of approximation error for the alternating direction scheme, stability, and convergence order are investigated.

Keywords: parabolic equations, delay, alternating direction method.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2011, 272, suppl. 1, S101–S118

Bibliographic databases:

Document Type: Article
UDC: 519.63
Received: 02.11.2009

Citation: A. V. Lekomtsev, V. G. Pimenov, “Convergence of the alternating direction method for the numerical solution of a heat conduction equation with delay”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 1, 2010, 102–118; Proc. Steklov Inst. Math. (Suppl.), 272, suppl. 1 (2011), S101–S118

Citation in format AMSBIB
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\by A.~V.~Lekomtsev, V.~G.~Pimenov
\paper Convergence of the alternating direction method for the numerical solution of a~heat conduction equation with delay
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2010
\vol 16
\issue 1
\pages 102--118
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2011
\vol 272
\issue , suppl. 1
\pages S101--S118
\crossref{https://doi.org/10.1134/S0081543811020088}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79954615503}


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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. V. G. Pimenov, “Chislennye metody resheniya evolyutsionnykh uravnenii s zapazdyvaniem”, Izv. IMI UdGU, 2012, no. 1(39), 103–104  mathnet
    2. E. E. Tashirova, “Skhodimost raznostnogo metoda dlya resheniya dvumernogo volnovogo uravneniya s nasledstvennostyu”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 25:1 (2015), 78–92  mathnet  elib
    3. Solodushkin S.I., Yumanova I.F., De Staelen R.H., “A Difference Scheme For Multidimensional Transfer Equations With Time Delay”, J. Comput. Appl. Math., 318:SI (2017), 580–590  crossref  mathscinet  zmath  isi  scopus
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