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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
Received: 17.03.2022
Revised: 24.03.2022
Accepted: 18.07.2022
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
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}
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