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 O(N−1)O(N−1).
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.
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
\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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https://www.mathnet.ru/eng/vyuru308
https://www.mathnet.ru/eng/vyuru/v9/i1/p130
This publication is cited in the following 7 articles:
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S. Noeiaghdam, D. N. Sidorov, A. I. Dreglea, “Fuzzy Volterra integral equations with piecewise continuous kernels: theory and numerical solution”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 50 (2024), 36–50
Ildar Muftahov, Denis Sidorov, Aleksei Zhukov, Dmitriy Karamov, Advances in Intelligent Systems and Computing, 1301, Progress in Intelligent Decision Science, 2021, 808
Samad Noeiaghdam, Denis Sidorov, Abdul-Majid Wazwaz, Nikolai Sidorov, Valery Sizikov, “The Numerical Validation of the Adomian Decomposition Method for Solving Volterra Integral Equation with Discontinuous Kernels Using the CESTAC Method”, Mathematics, 9:3 (2021), 260
Denis Sidorov, Daniil Panasetsky, Nikita Tomin, Dmitriy Karamov, Aleksei Zhukov, Ildar Muftahov, Aliona Dreglea, Fang Liu, Yong Li, “Toward Zero-Emission Hybrid AC/DC Power Systems with Renewable Energy Sources and Storages: A Case Study from Lake Baikal Region”, Energies, 13:5 (2020), 1226
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
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
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