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Matem. Mod., 2011, Volume 23, Number 3, Pages 127–138 (Mi mm3092)  

This article is cited in 2 scientific papers (total in 2 papers)

One-stage Rosenbrock method with complex coefficients and automatic time step evaluation

A. M. Zubanova, N. I. Kokonkovb, P. D. Shirkovc

a Dubna International University for Nature, Society, and Man
b Moscow Institute of Physics and Technology
c Dubna International University of Nature, Society and Man (Dmitrov Branch)

Abstract: Well-known one-stage Rosenbrock scheme with complex coefficients is generalized to the case which allows to make a simple estimation of the truncation error. New version of such a scheme preserves all properties of the old one (such as $A$-stability and $L$-decrementation) and makes possible to choose step of integration automatically with the use of correction procedure.
Testing of strategy of time step evaluation as well as of new method has been done with the use of well known and original nonlinear differential equations and systems of equations include nonlinear equation of the heat conduction.

Keywords: Rosenbrock methods, monotonous schemes, stiff problems, method of lines, automatic time step evaluation.

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English version:
Mathematical Models and Computer Simulations, 2011, 3:5, 596–603

Bibliographic databases:

Received: 28.06.2010

Citation: A. M. Zubanov, N. I. Kokonkov, P. D. Shirkov, “One-stage Rosenbrock method with complex coefficients and automatic time step evaluation”, Matem. Mod., 23:3 (2011), 127–138; Math. Models Comput. Simul., 3:5 (2011), 596–603

Citation in format AMSBIB
\Bibitem{ZubKokShi11}
\by A.~M.~Zubanov, N.~I.~Kokonkov, P.~D.~Shirkov
\paper One-stage Rosenbrock method with complex coefficients and automatic time step evaluation
\jour Matem. Mod.
\yr 2011
\vol 23
\issue 3
\pages 127--138
\mathnet{http://mi.mathnet.ru/mm3092}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2849302}
\transl
\jour Math. Models Comput. Simul.
\yr 2011
\vol 3
\issue 5
\pages 596--603
\crossref{https://doi.org/10.1134/S2070048211050139}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84928989926}


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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. A. M. Zubanov, P. D. Shirkov, “Numerical study of one-step lineary implicit methods which are L-equivalent to stiffly accurate two-stages Runge–Kutta schemes”, Math. Models Comput. Simul., 5:4 (2013), 350–355  mathnet  crossref  mathscinet  elib
    2. A. M. Zubanov, N. N. Kutrukhin, P. D. Shirkov, “O postroenii lineino neyavnykh skhem, $LN$-ekvivalentnykh neyavnym metodam Runge–Kutty”, Kompyuternye issledovaniya i modelirovanie, 4:3 (2012), 483–496  mathnet  crossref
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