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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2023, Volume 26, Number 1, Pages 1–16
DOI: https://doi.org/10.15372/SJNM20230101 (Mi sjvm825) 		 
Stability domains of an implicit method for the numerical solution of Abel type integral algebraic equations

O. S. Budnikovaab, M. N. Botoroevaab, G. K. Sokolovaab

a Irkutsk State University, Russia
b Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences, Irkutsk, Russia
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DOI: https://doi.org/10.15372/SJNM20230101
Abstract: This article is devoted to a study of the properties of an implicit method for Abel type integral algebraic equations. An Abel type integral equation with stiff components is used for examining the properties of these methods and the stability domains are constructed. Numerical calculations confirming the results obtained are performed. In this article, a fractional «stiff» problem is proposed to study the stability of the mathematical objects considered.
Key words: Abel type integral-algebraic equations, Volterra integral equations, $k$-step methods, stiff problem, stability domains.
Funding agency Grant number
Russian Science Foundation 22-11-00173
Received: 05.04.2022
Revised: 01.07.2022
Accepted: 23.11.2022
Document Type: Article
UDC: 519.642.5
Language: Russian
Citation: O. S. Budnikova, M. N. Botoroeva, G. K. Sokolova, “Stability domains of an implicit method for the numerical solution of Abel type integral algebraic equations”, Sib. Zh. Vychisl. Mat., 26:1 (2023), 1–16
Citation in format AMSBIB
\Bibitem{BudBotSok23}
\by O.~S.~Budnikova, M.~N.~Botoroeva, G.~K.~Sokolova
\paper Stability domains of an implicit method for the numerical solution of Abel type integral algebraic equations
\jour Sib. Zh. Vychisl. Mat.
\yr 2023
\vol 26
\issue 1
\pages 1--16
\mathnet{http://mi.mathnet.ru/sjvm825}
\crossref{https://doi.org/10.15372/SJNM20230101}
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