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Vestnik YuUrGU. Ser. Mat. Model. Progr., 2016, Volume 9, Issue 1, Pages 130–136 (Mi vyuru308)  

This article is cited in 2 scientific papers (total in 2 papers)

Short Notes

Solvability and numerical solutions of systems of nonlinear Volterra integral equations of the first kind with piecewise continuous kernels

I. R. Muftahova, D. N. Sidorovabc

a Irkutsk National Research Technical University, Irkutsk, Russian Federation
b Irkutsk State University, Irkutsk, Russian Federation
c Melentiev Energy Systems Institute, Siberian Branch of Russian Academy of Sciences, Irkutsk, Russian Federation

Abstract: The existence theorem for systems of nonlinear Volterra integral equations kernels of the first kind with piecewise continuous is proved. Such equations model evolving dynamical systems. A numerical method for solving nonlinear Volterra integral equations of the first kind with piecewise continuous kernels is proposed using midpoint quadrature rule. Also numerical method for solution of systems of linear Volterra equations of the first kind is described. The examples demonstrate efficiency of proposed algorithms. The accuracy of proposed numerical methods is $\mathcal{O}(N^{-1})$.

Keywords: Volterra integral equations; discontinuous kernel; ill-posed problem; evolving dynamical systems; quadrature; Dekker–Brent method.

Funding Agency
The authors are thankfull to Dr. A.N. Tynda for valuable comments and discussions of the results presented in this article. The second author is partly supported by the International science and technology cooperation program of China and Russia under Grant No. 2015DFA70580.


DOI: https://doi.org/10.14529/mmp160111

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Bibliographic databases:

UDC: 517.968
MSC: 45D05
Received: 27.11.2015
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Citation: I. R. Muftahov, D. N. Sidorov, “Solvability and numerical solutions of systems of nonlinear Volterra integral equations of the first kind with piecewise continuous kernels”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 9:1 (2016), 130–136

Citation in format AMSBIB
\Bibitem{MufSid16}
\by I.~R.~Muftahov, D.~N.~Sidorov
\paper Solvability and numerical solutions of systems of nonlinear Volterra integral equations of the first kind with piecewise continuous kernels
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2016
\vol 9
\issue 1
\pages 130--136
\mathnet{http://mi.mathnet.ru/vyuru308}
\crossref{https://doi.org/10.14529/mmp160111}
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\elib{https://elibrary.ru/item.asp?id=25717243}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. N. Tynda, D. N. Sidorov, I. R. Muftakhov, “Chislennyi metod resheniya sistem nelineinykh integralnykh uravnenii Volterra I roda s razryvnymi yadrami”, Zhurnal SVMO, 20:1 (2018), 55–63  mathnet  crossref  elib
    2. S. Noeiaghdam, D. N. Sidorov, I. R. Muftahov, A. V. Zhukov, “Control of accuracy on Taylor-collocation method for load leveling problem”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 30 (2019), 59–72  mathnet  crossref
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