The predictor-corrector method for modelling of self-oscillatory systems


Cite item

Abstract

In the work physically reasonable algorithm of numerical modeling of nonlinear oscillatory and self-oscillatory systems is offered. The algorithm is based on discrete in time model of the linear oscillator. Nonlinearity is considered by introduction to the oscillator of additional communications by the structural analysis of an initial system. For approximation of a temporary derivative in nonlinear communications it is offered to use the scheme of the prediction and correction. In spite of the fact that theoretically the algorithm has the second order of accuracy, within the numerical experiment with Van der Pol oscillator it shows the best results, than a standard method of the second order – the Heun’s method.

About the authors

V.V. Zaitsev

Samara National Research University

Author for correspondence.
Email: zaitsev@samsu.ru

References

  1. Bogolyubov N.N., Mitropol’skiy Yu.A. Asimptoticheskie metody v teorii nelineynykh kolebaniy. Izd. 4-e. [Asymptotical methods in nonlinear oscillations theory. 4th edition]. M.: Nauka, 1974. 504 p. [in Russian].Landa P.S. Nelinejnye kolebaniya i volny. Izd. 3-e. [Nonlinear oscillations and waves. 3rd edition]. M.: Librokom, 2015. 552 p. [in Russian].Samarskiy A.A., Mikhaylov A.P. Matematicheskoe modelirovanie [Mathematical modeling]. M.: FIZMATLIT, 2002. 302 p. [in Russian].Parker T.S., Chua L.O. Practical numerical algorithms for chaotic systems. NY: Springer-Verlag, 1989. 348 p. DOI: https://doi.org/10.1007/978-1-4612-3486-9 [in English].Hairer E., Nersett S., Wanner G. Reshenie obyknovennykh differentsial’nykh uravneniy. Nezhestkie zadachi [Solving ordinary differential equations.]. M.: Mir, 1990. 512 p. [in Russian].Zaytsev V.V., Shilin A.N. Otobrazheniya generatora Van der Polya–Dyuffinga v diskretnom vremeni [The mappings of Van der Pol – Duffing generator in discrete time].
  2. Vestnik Samarskogo universiteta. Estestvennonauchnaya seriya [Vestnik of Samara University. Natural Science Series], 2017, Vol. 23, no. 2, pp. 51–59 [in Russian].Zaytsev V.V., Karlov A.V., Karlov Ar.V. O chislennom modelirovanii tomsonovskikh avtokolebatel’nykh sistem [About numerical modelling of Thomson self-oscilla­tory systems]. Vestnik Samarskogo gosudarstvennogo universiteta. Estestvennonauchnaya seriya [Vestnik of Samara State University. Natural Science Series], 2015, Vol. 21, no. 6, pp. 141–150 [in Russian].Kuznetsov A.P., Savin A.V., Sedova Yu.V. Bifurkatsiya Bogdanova–Takensa: ot nepreryvnoy k diskretnoy modeli [Bogdanov–Takens bifurcation:from flows to discrete systems]. Izvestiya vuzov. Prikladnaya nelineynaya dinamika [Izvestiya VUZ. Appled nonlinear dynamics], 2009, Vol. 17, no. 6, pp. 39–158 [in Russian].Anishhenko V.S. , Astakhov V.V., Vadivasova T.E., Neiman A.B., Strelkova G.I., Schimanskii-Gaier L. Nelineynye effekty v khaoticheskikh i stokhasticheskikh sistemakh [Nonlinear effects in chaotic and stochastic systems]. Moskva; Izhevsk: Institut komp’yuternykh issledovaniy, 2003, 544 p. [in Russian].Nefedov V.I., Reshetnyak S.A., Tret’yakov G.N., Zasovin E.A. Fil’tratsiya signalov na fone shuma vblizi attraktora [Filtration of a signal against the background of noise near an attractor]. Radiotekhnika i elektronika [Journal of Communications Technology and Electronics], 2019, Vol. 64, no. 2. pp. 175–180. DOI: https://doi.org/10.1134/S0033849419020165 [in Russian].Balakin M.I., Ryskin N.M. Multistabil’ost’i slozhnye kolebatel’nye rezhimy v generatore s zapazdyvayushhim otrazheniem ot nagruzki [Multistabilnost and the difficult oscillatory modes in the generator with the late reflection from loading]. Pisma v ZHTF [Letters in ZhTF], 2019, Vol. 45, issue 6, pp. 33–35. DOI: https://doi.org/10.21883/PJTF.2019.06.47497.17551 [in Russian].Zaitsev V.V., Stulov I.V. O vliyanii podmenennykh garmonik na dinamiku avtokolebanij v diskretnom vremeni [About influence of the changed harmonics on dynamics of self-oscillations in discrete time]. Izvestiya vuzov. Prikladnaya nelinejnaya dinamika [Izvestiya VUZ. Appled nonlinear dynamics], 2015, Vol. 23, no 6, pp. 40–46. DOI: https://doi.org/10.18500/0869-6632-2015-23-6-40-46 [in Russian].

Copyright (c) 2019 Zaitsev V.

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies