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Matematicheskie Zametki, 2022, Volume 111, Issue 4, Pages 581–591
DOI: https://doi.org/10.4213/mzm13303 (Mi mzm13303) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On the Dynamic Solution of the Volterra Integral Equation in the Form of Rational Spline Functions

A.-R. K. Ramazanovab, A. K. Ramazanovc, V. G. Magomedovaa

a Daghestan State University, Makhachkala
b Daghestan Scientific Centre of Russian Academy of Sciences, Makhachkala
c Kaluga Branch of Bauman Moscow State Technical University
Full-text PDF (464 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm13303
Abstract: The approximate solution of the Volterra integral equation of the second kind is represented as collocation rational spline functions on successive closed intervals exhausting the entire solution domain. Estimates for the rate of convergence of approximate solutions to the exact solution in the uniform metric are also obtained via the modulus of continuity of the solution and its derivatives of first and second order.
Keywords: rational spline functions, Volterra equation, collocation method.
Received: 23.09.2021
Revised: 23.11.2021
English version:
Mathematical Notes, 2022, Volume 111, Issue 4, Pages 595–603
DOI: https://doi.org/10.1134/S0001434622030282
Bibliographic databases:
Document Type: Article
UDC: 519.64+519.65
Language: Russian
Citation: A.-R. K. Ramazanov, A. K. Ramazanov, V. G. Magomedova, “On the Dynamic Solution of the Volterra Integral Equation in the Form of Rational Spline Functions”, Mat. Zametki, 111:4 (2022), 581–591; Math. Notes, 111:4 (2022), 595–603
Citation in format AMSBIB
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\by A.-R.~K.~Ramazanov, A.~K.~Ramazanov, V.~G.~Magomedova
\paper On the Dynamic Solution of the Volterra Integral Equation in the Form of Rational Spline Functions
\jour Mat. Zametki
\yr 2022
\vol 111
\issue 4
\pages 581--591
\mathnet{http://mi.mathnet.ru/mzm13303}
\crossref{https://doi.org/10.4213/mzm13303}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4461287}
\transl
\jour Math. Notes
\yr 2022
\vol 111
\issue 4
\pages 595--603
\crossref{https://doi.org/10.1134/S0001434622030282}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85128980065}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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