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.
This work is partially supported by Russian Foundation of Basic Research (grant 14-01-00047).
Received: 10.11.2015 Received in revised form: 15.01.2016 Accepted: 20.02.2016
Bibliographic databases:
Document Type:
Article
UDC:519.622
Language: English
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
\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{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000412008200010}
Linking options:
https://www.mathnet.ru/eng/jsfu478
https://www.mathnet.ru/eng/jsfu/v9/i2/p209
This publication is cited in the following 3 articles:
E. B. Kuznetsov, S. S. Leonov, E. D. Tsapko, “Estimating the domain of absolute stability of a numerical scheme based on the method of solution continuation with respect to a parameter for solving stiff initial value problems”, Comput. Math. Math. Phys., 63:4 (2023), 528–541
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
Yury Shornikov, Evgeny Popov, 2019 International Seminar on Electron Devices Design and Production (SED), 2019, 1
Citation in format AMSBIB
Contact us: