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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2011, Issue 3(24), Pages 100–107 (Mi vsgtu920)  

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

Mathematical Modeling

Maximal order of accuracy of $(m, 1)$-methods for solving stiff problems

E. A. Novikovab

a Dept. of Computational Mathematics, Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences, Krasnoyarsk
b Dept. of Mathematical Software for Systems and Discrete Devices, Siberian Federal University, Krasnoyarsk

Abstract: We investigate $(m, 1)$-methods for solving stiff problems in which the right part of system of the differential equations is calculated one times on each step. It is shown that the maximal order of accuracy of the $L$-stability $(m, 1)$-method is equal to two, and the method of the maximal order is constructed.

Keywords: stiff problems, Rosenbrock schemes, $(m, k)$-methods, $A$-stability, $L$-stability

DOI: https://doi.org/10.14498/vsgtu920

Full text: PDF file (211 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 519.622
MSC: Primary 65L20; Secondary 65L05, 34A34
Original article submitted 28/I/2011
revision submitted – 17/VIII/2011

Citation: E. A. Novikov, “Maximal order of accuracy of $(m, 1)$-methods for solving stiff problems”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 3(24) (2011), 100–107

Citation in format AMSBIB
\Bibitem{Nov11}
\by E.~A.~Novikov
\paper Maximal order of accuracy of $(m, 1)$-methods for solving stiff problems
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2011
\vol 3(24)
\pages 100--107
\mathnet{http://mi.mathnet.ru/vsgtu920}
\crossref{https://doi.org/10.14498/vsgtu920}


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    This publication is cited in the following articles:
    1. S. A. Konev, “Rasshirenie teorii kornevykh derevev Butchera dlya uproschënnogo $(m,k)$-metoda”, Preprinty IPM im. M. V. Keldysha, 2019, 023, 26 pp.  mathnet  crossref  elib
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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