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Vestnik YuUrGU. Ser. Mat. Model. Progr., 2014, Volume 7, Issue 3, Pages 107–115 (Mi vyuru150)  

This article is cited in 5 scientific papers (total in 5 papers)

Programming & Computer Software

Numerical Solution of Volterra Integral Equations of the First Kind with Piecewise Continuous Kernel

D. N. Sidorovabc, A. N. Tyndad, I. R. Muftahovc

a Irkutsk State University
b Energy Systems Institute, Siberian Branch of Russian Academy of Sciences, Irkutsk, Russian Federation
c Irkutsk State Technical University, Irkutsk, Russian Federation
d Penza State University, Penza, Russian Federation

Abstract: Integral equations are in the core of many mathematical models in physics, economics and ecology. Volterra integral equations of the first kind with jump discontinuous kernels play important role in such models and they are considered in this article. Regularization method and sufficient conditions are derived for existence and uniqueness of the solution of such integral equations. An efficient numerical method based on the mid-rectangular quadrature rule is proposed for these equations with jump discontinuous kernels. The accuracy of proposed numerical method is $\mathcal{O}(N^{-1})$. The model examples demonstrate efficiency of proposed method: errors, two mesh differences and orders of convergent.

Keywords: Volterra integral equations of the 1st kind; evolving systems; Glushkov integral model; numerical method.

DOI: https://doi.org/10.14529/mmp140311

Full text: PDF file (323 kB)
References: PDF file   HTML file

UDC: 517.968
MSC: 45D05
Received: 20.05.2014

Citation: D. N. Sidorov, A. N. Tynda, I. R. Muftahov, “Numerical Solution of Volterra Integral Equations of the First Kind with Piecewise Continuous Kernel”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 7:3 (2014), 107–115

Citation in format AMSBIB
\Bibitem{SidTynMuf14}
\by D.~N.~Sidorov, A.~N.~Tynda, I.~R.~Muftahov
\paper Numerical Solution of Volterra Integral Equations of the First Kind with Piecewise Continuous Kernel
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2014
\vol 7
\issue 3
\pages 107--115
\mathnet{http://mi.mathnet.ru/vyuru150}
\crossref{https://doi.org/10.14529/mmp140311}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. A. Sidorov, D. N. Sidorov, I. R. Muftakhov, “O roli metoda vozmuschenii i teoremy Banakha–Shteingauza v voprosakh regulyarizatsii uravnenii pervogo roda”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 14 (2015), 82–99  mathnet
    2. 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”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 9:1 (2016), 130–136  mathnet  crossref  elib
    3. I. R. Muftakhov, D. N. Sidorov, N. A. Sidorov, “O regulyarizatsii po Lavrentevu integralnykh uravnenii pervogo roda v prostranstve nepreryvnykh funktsii”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 15 (2016), 62–77  mathnet
    4. 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
    5. 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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