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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2006, Volume 46, Number 2, Pages 295–306 (Mi zvmmf522)  
This article is cited in 12 scientific papers (total in 12 papers)

Two-step iterative methods for solving the stationary convection-diffusion equation with a small parameter at the highest derivative on a uniform grid

Zh. Zh. Baia, L. A. Krukierb, T. S. Martynovab

a State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Science, 100080, P.O. Box 2719, Beijing, P. R. China
b Computer Center of Rostov State University, pr. Stachki 200/1, bld. 2, Rostov-on-Don, 344090, Russia
Full-text PDF (1290 kB) Citations (12)
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Abstract: A stationary convection-diffusion problem with a small parameter multiplying the highest derivative is considered. The problem is discretized on a uniform rectangular grid by the central-difference scheme. A new class of two-step iterative methods for solving this problem is proposed and investigated. The convergence of the methods is proved, optimal iterative methods are chosen, and the rate of convergence is estimated. Numerical results are presented that show the high efficiency of the methods.
Key words: iterative methods, dissipative matrix, convergence, optimal iterative parameters, transition operator.
Received: 18.04.2005
English version:
Computational Mathematics and Mathematical Physics, 2006, Volume 46, Issue 2, Pages 282–293
DOI: https://doi.org/10.1134/S0965542506020102
Bibliographic databases:
Document Type: Article
UDC: 519.63
Language: Russian
Citation: Zh. Zh. Bai, L. A. Krukier, T. S. Martynova, “Two-step iterative methods for solving the stationary convection-diffusion equation with a small parameter at the highest derivative on a uniform grid”, Zh. Vychisl. Mat. Mat. Fiz., 46:2 (2006), 295–306; Comput. Math. Math. Phys., 46:2 (2006), 282–293
Citation in format AMSBIB
\Bibitem{BaiKruMar06}
\by Zh.~Zh.~Bai, L.~A.~Krukier, T.~S.~Martynova
\paper Two-step iterative methods for solving the stationary convection-diffusion equation with a~small parameter at the highest derivative on a~uniform grid
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 2
\pages 295--306
\mathnet{http://mi.mathnet.ru/zvmmf522}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=2239766}
\zmath{https://zbmath.org/?q=an:05200904}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 2
\pages 282--293
\crossref{https://doi.org/10.1134/S0965542506020102}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746032903}
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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