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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2024, Volume 519, Pages 53–56
DOI: https://doi.org/10.31857/S2686954324050103 (Mi danma565) 		 
This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

Analytic method for solving one class of nonlinear equations

Yu. S. Popkovab

a Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, Moscow, Russia
b V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia
Full-text PDF Citations (1)
DOI: https://doi.org/10.31857/S2686954324050103
Abstract: The paper proposes an analytical approximate method for calculating multidimensional integrals of analytic integrand functions, using the approximation of the latter by a power series. This approach lets transforming the original system of nonlinear equations with integral components into a system of equations with a polynomial left-hand side. To solve equations of this class we developed an analytical method. A sequential recurrent procedure has been developed for the analytical solution of this class of nonlinear equations.
Keywords: integral components, analytic functions, Taylor–Macloren power series, implicit functions, parametric families of nonlinear equations.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2024-544
This work was supported by the Ministry of Science and Higher Education of the Russian Federation, project no. 075-15-2024-544.
Received: 05.06.2024
Revised: 11.07.2024
Accepted: 23.08.2024
English version:
Doklady Mathematics, 2024, Volume 110, Issue 2, Pages 404–407
DOI: https://doi.org/10.1134/S1064562424601392
Bibliographic databases:
Document Type: Article
UDC: 517.54
Language: Russian
Citation: Yu. S. Popkov, “Analytic method for solving one class of nonlinear equations”, Dokl. RAN. Math. Inf. Proc. Upr., 519 (2024), 53–56; Dokl. Math., 110:2 (2024), 404–407
Citation in format AMSBIB
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\by Yu.~S.~Popkov
\paper Analytic method for solving one class of nonlinear equations
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2024
\vol 519
\pages 53--56
\mathnet{http://mi.mathnet.ru/danma565}
\crossref{https://doi.org/10.31857/S2686954324050103}
\elib{https://elibrary.ru/item.asp?id=75994116}
\transl
\jour Dokl. Math.
\yr 2024
\vol 110
\issue 2
\pages 404--407
\crossref{https://doi.org/10.1134/S1064562424601392}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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