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Matem. Mod., 2011, Volume 23, Number 3, Pages 139–160 (Mi mm3093)  

This article is cited in 1 scientific paper (total in 1 paper)

About one new two-stages Rosenbrock scheme for differential-algebraic systems

A. B. Alshin, E. A. Alshina

Moscow Institute of Electronic Technology (Technical University), Zelenograd

Abstract: The equations for coefficients of two-stages Rosenbrock scheme guarantying approximation with third order of accuracy for differential-algebraic system (index 1) are obtained in this paper. These coefficients are complex numbers. New 2-stages Rosenbrock scheme is constructed. It is L2-stable. This scheme has accuracy $O(\tau^3)$ for differential-algebraic systems and $O(\tau^4)$ for pure differential stiff systems. Convergence of this scheme is proved. This scheme was tested on several standard stiff tests and compared with previously know scheme of the same class.

Keywords: stiff-system, differential-algebraic systems, Rosenbrock schemes, schemes with complex parameters, A-stability, L-stability.

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English version:
Mathematical Models and Computer Simulations, 2011, 3:5, 604–618

Bibliographic databases:

Received: 23.03.2010

Citation: A. B. Alshin, E. A. Alshina, “About one new two-stages Rosenbrock scheme for differential-algebraic systems”, Matem. Mod., 23:3 (2011), 139–160; Math. Models Comput. Simul., 3:5 (2011), 604–618

Citation in format AMSBIB
\Bibitem{AlsAls11}
\by A.~B.~Alshin, E.~A.~Alshina
\paper About one new two-stages Rosenbrock scheme for differential-algebraic systems
\jour Matem. Mod.
\yr 2011
\vol 23
\issue 3
\pages 139--160
\mathnet{http://mi.mathnet.ru/mm3093}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2849303}
\transl
\jour Math. Models Comput. Simul.
\yr 2011
\vol 3
\issue 5
\pages 604--618
\crossref{https://doi.org/10.1134/S2070048211050024}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84928993116}


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    This publication is cited in the following articles:
    1. Bulatov M., Solovarova L., “Collocation-Variation Difference Schemes With Several Collocation Points For Differential-Algebraic Equations”, Appl. Numer. Math., 149:SI (2020), 153–163  crossref  mathscinet  isi
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