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Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 2, Pages 295–306 (Mi zvmmf522)  

This article is cited in 10 scientific papers (total in 10 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

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.

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English version:
Computational Mathematics and Mathematical Physics, 2006, 46:2, 282–293

Bibliographic databases:

UDC: 519.63
Received: 18.04.2005

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{http://www.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{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746032903}


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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. T. S. Martynova, “Numerical solution of second order elliptical equations with mixed derivatives by effective iterative methods”, Math. Models Comput. Simul., 1:3 (2009), 370–382  mathnet  crossref  mathscinet  zmath
    2. Krukier L.A., Martynova T.S., Bai Zh.-Zh., “Product-type skew-Hermitian triangular splitting iteration methods for strongly non-Hermitian positive definite linear systems”, Journal of Computational and Applied Mathematics, 232:1 (2009), 3–16  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. Muratova G.V., Andreeva E.M., “Multigrid method for solving convection-diffusion problems with dominant convection”, Journal of Computational and Applied Mathematics, 226:1 (2009), 77–83  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. Kadalbajoo M.K., Gupta V., “A brief survey on numerical methods for solving singularly perturbed problems”, Applied Mathematics and Computation, 217:8 (2010), 3641–3716  crossref  mathscinet  zmath  isi  scopus
    5. Cao Ya., Jiang M.-Q., Zheng Y.-L., “A Note on the Positive Stable Block Triangular Preconditioner for Generalized Saddle Point Problems”, Appl. Math. Comput., 218:22 (2012), 11075–11082  crossref  mathscinet  zmath  isi  elib  scopus
    6. L. A. Krukier, T. S. Martynova, “An effective iterative method for saddle point problems”, Math. Models Comput. Simul., 7:4 (2015), 331–338  mathnet  crossref  elib
    7. Bai Zh.-Zh., Hadjidimos A., “Optimization of Extrapolated Cayley Transform With Non-Hermitian Positive Definite Matrix”, Linear Alg. Appl., 463 (2014), 322–339  crossref  mathscinet  zmath  isi  elib  scopus
    8. Muratova G., Andreeva E., “Multigrid Method For Fluid Dynamic Problems”, J. Comput. Math., 32:3 (2014), 233–247  crossref  mathscinet  zmath  isi  elib  scopus
    9. T. S. Martynova, L. A. Krukier, “Chislennoe reshenie nelineinoi zadachi o naimenshikh kvadratakh, voznikayuschei pri issledovanii zagryaznyayuschikh veschestv v okruzhayuschei srede”, Matem. modelirovanie, 28:8 (2016), 82–96  mathnet  elib
    10. L. A. Krukier, T. S. Martynova, “Preconditioning of GMRES by the skew-Hermitian iterations”, Num. Anal. Appl., 9:3 (2016), 207–217  mathnet  crossref  crossref  mathscinet  isi  elib  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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