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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2018, Volume 154, Pages 89–98 (Mi into382)  
This article is cited in 11 scientific papers (total in 11 papers)

On a Certain Finite-Difference Scheme for a Hereditary Oscillatory Equation

R. I. Parovikab

a Institute of Cosmophysical Researches and Radio Wave Propagation, Far East Division, Russian Academy of Sciences
b Kamchatka State University named after Vitus Bering
Full-text PDF (203 kB) Citations (11)
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Abstract: In this paper, we proposed an explicit finite-difference scheme for numerical simulation of the Cauchy problem for a nonlinear integro-differential equation that describes an oscillatory process with friction and memory (heredity) and the corresponding local initial conditions. Approximation, stability, and convergence of the finite-difference scheme are examined. Results of computer experiments that implement the numerical scheme proposed confirm theoretical estimates.
Keywords: stability, convergence, explicit finite-difference scheme, heredity, integro-differential equation, memory function, Runge rule, approximation.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation AAAA-A17-117031050058-9
This work was supported by the Ministry of Science and Education of the Russian Federation within the framework of the Government assignment “Applications of fractional calculus in the theory of oscillatory processes” (project AAAA-A17-117031050058-9).
English version:
Journal of Mathematical Sciences (New York), 2021, Volume 253, Issue 4, Pages 547–557
DOI: https://doi.org/10.1007/s10958-021-05252-2
Bibliographic databases:
Document Type: Article
UDC: 517.962
MSC: 37M05, 34A08
Language: Russian
Citation: R. I. Parovik, “On a Certain Finite-Difference Scheme for a Hereditary Oscillatory Equation”, Proceedings of the International Conference “Actual Problems of Applied Mathematics and Physics,” Kabardino-Balkaria, Nalchik, May 17–21, 2017, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 154, VINITI, Moscow, 2018, 89–98; J. Math. Sci. (N. Y.), 253:4 (2021), 547–557
Citation in format AMSBIB
\Bibitem{Par18}
\by R.~I.~Parovik
\paper On a Certain Finite-Difference Scheme for a Hereditary Oscillatory Equation
\inbook Proceedings of the International Conference “Actual Problems of Applied Mathematics and Physics,” Kabardino-Balkaria, Nalchik, May 17–21, 2017
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2018
\vol 154
\pages 89--98
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into382}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3904971}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2021
\vol 253
\issue 4
\pages 547--557
\crossref{https://doi.org/10.1007/s10958-021-05252-2}
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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