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Vestnik Yuzhno-Ural'skogo Universiteta. Seriya Matematicheskoe Modelirovanie i Programmirovanie, 2016, Volume 9, Issue 1, Pages 130–136
DOI: https://doi.org/10.14529/mmp160111 (Mi vyuru308) 		 
This article is cited in 7 scientific papers (total in 7 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
Full-text PDF (486 kB) Citations (7)
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DOI: https://doi.org/10.14529/mmp160111
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.
Received: 27.11.2015
Bibliographic databases:
Document Type: Article
UDC: 517.968
MSC: 45D05
Language: English
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
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\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
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\crossref{https://doi.org/10.14529/mmp160111}
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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