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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2006, Volume 46, Number 8, Pages 1392–1414 (Mi zvmmf426)  
This article is cited in 51 scientific papers (total in 51 papers)

Rosenbrock schemes with complex coefficients for stiff and differential algebraic systems

A. B. Alshina, E. A. Alshinaa, N. N. Kalitkinb, A. B. Koryaginac

a Faculty of Physics, Moscow State University, Leninskie gory, Moscow, 119992, Russia
b Institute of Mathematical Modeling, Russian Academy of Sciences, Miusskaya pl. 4a, Moscow, 125047, Russia
c Moscow State Institute of Electronic Engineering, Technical University, Zelenograd, Moscow, 103498, Russia
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Abstract: Many applied problems are described by differential algebraic systems. Complex Rosenbrock schemes are proposed for the numerical integration of differential algebraic systems by the $\varepsilon$-embedding method. The method is proved to converge quadratically. The scheme is shown to be applicable even to superstiff systems. The method makes it possible to perform computations with a guaranteed accuracy. An equation is derived that describes the leading term of the error in the method as a function of time. An algorithm extending the method to systems of differential equations for complex-valued functions is proposed. Examples of numerical computations are given.
Key words: systems of stiff differential algebraic equations, Rosenbrock scheme with complex coefficients.
Received: 24.03.2006
English version:
Computational Mathematics and Mathematical Physics, 2006, Volume 46, Issue 8, Pages 1320–1340
DOI: https://doi.org/10.1134/S0965542506080057
Bibliographic databases:
Document Type: Article
UDC: 519.622.2
Language: Russian
Citation: A. B. Alshin, E. A. Alshina, N. N. Kalitkin, A. B. Koryagina, “Rosenbrock schemes with complex coefficients for stiff and differential algebraic systems”, Zh. Vychisl. Mat. Mat. Fiz., 46:8 (2006), 1392–1414; Comput. Math. Math. Phys., 46:8 (2006), 1320–1340
Citation in format AMSBIB
\Bibitem{AlsAlsKal06}
\by A.~B.~Alshin, E.~A.~Alshina, N.~N.~Kalitkin, A.~B.~Koryagina
\paper Rosenbrock schemes with complex coefficients for stiff and differential algebraic systems
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 8
\pages 1392--1414
\mathnet{http://mi.mathnet.ru/zvmmf426}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2287358}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 8
\pages 1320--1340
\crossref{https://doi.org/10.1134/S0965542506080057}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33748314587}
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    • This publication is cited in the following 51 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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