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Vestnik Yuzhno-Ural'skogo Universiteta. Seriya Matematicheskoe Modelirovanie i Programmirovanie, 2017, Volume 10, Issue 1, Pages 138–148
DOI: https://doi.org/10.14529/mmp170109 (Mi vyuru363) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Programming & Computer Software

Mathematical modelling of hereditarity Airy oscillator with friction

R. I. Parovikab

a Kamchatka State University by Vitus Bering, Petropavlovsk-Kamchatsky
b Institute Space Physics Research and Radio Wave Propagation FEB RAS, Kamchatka region, Paratunka, Russian Federation
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DOI: https://doi.org/10.14529/mmp170109
Abstract: Work is devoted to mathematical modelling hereditarity oscillatory systems with the help of the mathematical apparatus of fractional calculus on the example of an Airy oscillator with friction. Model Airy equation was written in terms of Gerasimov–Caputo fractional derivatives. Next a finite-difference scheme to this generalized equation for numerical computation was proposed. The problems of approximation, stability and convergence of a numerical scheme are considered. The results of simulations are presented based on numerical solutions waveforms and phase trajectories depending on different values of the control parameters are built.
Keywords: Airy oscillator; hereditarity; Gerasimov–Caputo derivative; finite-difference scheme; the phase trajectory.
Received: 15.05.2016
Bibliographic databases:
Document Type: Article
UDC: 517.925.42
MSC: 37C70
Language: Russian
Citation: R. I. Parovik, “Mathematical modelling of hereditarity Airy oscillator with friction”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 10:1 (2017), 138–148
Citation in format AMSBIB
\Bibitem{Par17}
\by R.~I.~Parovik
\paper Mathematical modelling of hereditarity Airy oscillator with friction
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2017
\vol 10
\issue 1
\pages 138--148
\mathnet{http://mi.mathnet.ru/vyuru363}
\crossref{https://doi.org/10.14529/mmp170109}
\elib{https://elibrary.ru/item.asp?id=28922156}
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    • This publication is cited in the following 5 articles:
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