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Vestnik YuUrGU. Ser. Mat. Model. Progr., 2017, Volume 10, Issue 1, Pages 138–148 (Mi vyuru363)  

This article is cited in 2 scientific papers (total in 2 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

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.

DOI: https://doi.org/10.14529/mmp170109

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Bibliographic databases:

UDC: 517.925.42
MSC: 37C70
Received: 15.05.2016

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{http://elibrary.ru/item.asp?id=28922156}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. R. I. Parovik, “Suschestvovanie i edinstvennost zadachi Koshi dlya shirokogo klassa ereditarnykh ostsillyatorov”, Mezhdunar. nauch.-issled. zhurn., 2017, no. 10-3(64), 112–115  mathnet  crossref
    2. R. I. Parovik, “Mathematical model of a wide class memory oscillators”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 11:2 (2018), 108–122  mathnet  crossref  elib
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