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Vestnik YuUrGU. Ser. Mat. Model. Progr., 2020, Volume 13, Issue 4, Pages 58–65 (Mi vyuru571)  

Mathematical Modelling

Numerical analysis of fractional order integral dynamical models with piecewise continuous kernels

A. Tyndaa, D. Sidorovbc, I. Muftahovbd

a Penza State University, Penza, Russian Federation
b Melentiev Energy Systems Institute SB RAS, Irkutsk, Russian Federation
c Irkutsk National Research Technical University, Irkutsk, Russian Federation
d Main Computing Center of JSC Russian Railways, Irkutsk, Russian Federation

Abstract: Volterra integral equations find their application in many areas, including mathematical physics, control theory, mechanics, electrical engineering, and in various industries. In particular, dynamic Volterra models with discontinuous kernels are effectively used in power engineering to determine the operating modes of energy storage devices, as well as to solve the problem of load balancing. This article proposes the numerical scheme for solution of the fractional order linear Volterra integral equations of the first kind with piecewise continuous kernels. The developed approach is based on a polynomial collocation method and effectively approximate such a weakly singular integrals. The efficiency of proposed numerical scheme is illustrated by two examples.

Keywords: Volterra integral equations, numerical method, convergence, discontinuous kernel, singularity, fractional integral.

Funding Agency Grant Number
Ministry of Science and Higher Education of the Russian Federation FZZS-2020-0039
This work was partially supported by the base part of the Government Assignment for Scientific Research from the Ministry of Science and Higher Education of Russia (project code: FZZS-2020-0039).


DOI: https://doi.org/10.14529/mmp200405

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UDC: 517.968.22
MSC: 45D05, 34A08, 65R20
Received: 05.10.2020
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Citation: A. Tynda, D. Sidorov, I. Muftahov, “Numerical analysis of fractional order integral dynamical models with piecewise continuous kernels”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 13:4 (2020), 58–65

Citation in format AMSBIB
\Bibitem{TynSidMuf20}
\by A.~Tynda, D.~Sidorov, I.~Muftahov
\paper Numerical analysis of fractional order integral dynamical models with piecewise continuous kernels
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2020
\vol 13
\issue 4
\pages 58--65
\mathnet{http://mi.mathnet.ru/vyuru571}
\crossref{https://doi.org/10.14529/mmp200405}


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