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J. Sib. Fed. Univ. Math. Phys., 2016, Volume 9, Issue 2, Pages 209–219 (Mi jsfu478)  

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

Application of explicit methods with extended stability regions for solving stiff problems

Eugeny A. Novikova, Mikhail V. Rybkovb

a Institute of Computational Modeling SB RAS, Akademgorodok, 50/44, Krasnoyarsk, 660036, Russia
b Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041, Russia

Abstract: An algorithm is developed to determine coefficients of the stability polynomials such that the explicit Runge–Kutta methods have a predetermined shape and size of the stability region. Inequalities for accuracy and stability control are obtained. The impact of the stability control on efficiency of explicit methods to solving stiff problems is shown. Numerical calculations confirm that the three-step method of the first order with extended stability region is more efficient than the traditional three-stage method of the third order.

Keywords: stiff problem, explicit methods, stability region, accuracy and stability control.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00047_а
This work is partially supported by Russian Foundation of Basic Research (grant 14-01-00047).


DOI: https://doi.org/10.17516/1997-1397-2016-9-2-209-219

Full text: PDF file (232 kB)
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Bibliographic databases:

UDC: 519.622
Received: 10.11.2015
Received in revised form: 15.01.2016
Accepted: 20.02.2016
Language:

Citation: Eugeny A. Novikov, Mikhail V. Rybkov, “Application of explicit methods with extended stability regions for solving stiff problems”, J. Sib. Fed. Univ. Math. Phys., 9:2 (2016), 209–219

Citation in format AMSBIB
\Bibitem{NovRyb16}
\by Eugeny~A.~Novikov, Mikhail~V.~Rybkov
\paper Application of explicit methods with extended stability regions for solving stiff problems
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2016
\vol 9
\issue 2
\pages 209--219
\mathnet{http://mi.mathnet.ru/jsfu478}
\crossref{https://doi.org/10.17516/1997-1397-2016-9-2-209-219}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000412008200010}


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    This publication is cited in the following articles:
    1. Yu. Shornikov, E. Popov, “Modeling and simulation of transients in electric power systems using hybrid system theory”, Amcse 2018 - International Conference on Applied Mathematics, Computational Science and Systems Engineering, Itm Web of Conferences, 24, ed. N. Bardis, EDP Sciences, 2019, UNSP 02012  crossref  isi
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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