Abstract:
In this paper, we consider a class of second order systems of the Volterra nonlinear integral equations. This class is related to the automatic control problem of a dynamic object with vector inputs and outputs. A numerical solution technique based on the Newton–Kantorovich method is considered. To verify the efficiency of the algorithms developed, a series of test calculations were carried out.
Key words:
systems of the polynomial Volterra equations of the first kind, numerical solution, Newton–Kantorovich method.
Citation:
S. V. Solodusha, “To the numerical solution of one class of systems of the Volterra polynomial equations of the first kind”, Sib. Zh. Vychisl. Mat., 21:1 (2018), 117–126; Num. Anal. Appl., 11:1 (2018), 89–97
\Bibitem{Sol18}
\by S.~V.~Solodusha
\paper To the numerical solution of one class of systems of the Volterra polynomial equations of the first kind
\jour Sib. Zh. Vychisl. Mat.
\yr 2018
\vol 21
\issue 1
\pages 117--126
\mathnet{http://mi.mathnet.ru/sjvm672}
\crossref{https://doi.org/10.15372/SJNM20180108}
\elib{https://elibrary.ru/item.asp?id=32466484}
\transl
\jour Num. Anal. Appl.
\yr 2018
\vol 11
\issue 1
\pages 89--97
\crossref{https://doi.org/10.1134/S1995423918010093}
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Linking options:
https://www.mathnet.ru/eng/sjvm672
https://www.mathnet.ru/eng/sjvm/v21/i1/p117
This publication is cited in the following 5 articles:
Valery Sizikov, Nina Rushchenko, ““Spectral Method” for Determining a Kernel of the Fredholm Integral Equation of the First Kind of Convolution Type and Suppressing the Gibbs Effect”, Mathematics, 12:1 (2023), 13
S. Solodusha, M. Bulatov, “Integral equations related to Volterra series and inverse problems: elements of theory and applications in heat power engineering”, Mathematics, 9:16 (2021), 1905
Yu Voskoboinikov, V Boeva, “Synthesis of a smoothing bicubic spline for differentiating experimental data of nonparametric identification”, J. Phys.: Conf. Ser., 2131:3 (2021), 032023
S. V. Solodusha, “Identification of input signals in integral models of one class of nonlinear dynamic systems”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 30 (2019), 73–82
Citation in format AMSBIB
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