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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2022, Volume 25, Number 4, Pages 417–428
DOI: https://doi.org/10.15372/SJNM20220407 (Mi sjvm821) 		 
Stability domains of explicit multistep methods

I. V. Kireevab, A. E. Novikovb, E. A. Novikovba

a Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences, Krasnoyarsk
b Institute of Mathematics and Computer Science, Siberian Federal University, Krasnoyarsk
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DOI: https://doi.org/10.15372/SJNM20220407
Abstract: A new algorithm is proposed for obtaining stability domains of multistep numerical schemes. The algorithm is based on Bernoulli’s algorithm for computing the greatest in magnitude root of a polynomial with complex coefficients and the Dandelin–Lobachevsky–Graeffe method for squaring the roots. Numerical results on the construction of stability domains of Adams–Bashforth methods of order 3–11 are given.
Key words: Adams–Bashforth method, locus, stability domain, Bernoulli method, Dandelin–Lobachevsky–Graeffe method.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-02-2022-873
This work is supported by the Krasnoyarsk Mathematical Center and financed by the Ministry of Science and Higher Education of the Russian Federation in the framework of the establishment and development of regional Centers for Mathematics Research and Education (Agreement no. 075-02-2022-873).
Received: 17.03.2022
Revised: 24.03.2022
Accepted: 18.07.2022
English version:
Numerical Analysis and Applications, 2022, Volume 15, Issue 4, Pages 343–352
DOI: https://doi.org/10.1134/S1995423922040073
Document Type: Article
UDC: 519.6
Language: Russian
Citation: I. V. Kireev, A. E. Novikov, E. A. Novikov, “Stability domains of explicit multistep methods”, Sib. Zh. Vychisl. Mat., 25:4 (2022), 417–428; Num. Anal. Appl., 15:4 (2022), 343–352
Citation in format AMSBIB
\Bibitem{KirNovNov22}
\by I.~V.~Kireev, A.~E.~Novikov, E.~A.~Novikov
\paper Stability domains of explicit multistep
methods
\jour Sib. Zh. Vychisl. Mat.
\yr 2022
\vol 25
\issue 4
\pages 417--428
\mathnet{http://mi.mathnet.ru/sjvm821}
\crossref{https://doi.org/10.15372/SJNM20220407}
\transl
\jour Num. Anal. Appl.
\yr 2022
\vol 15
\issue 4
\pages 343--352
\crossref{https://doi.org/10.1134/S1995423922040073}
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