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Sib. Zh. Vychisl. Mat., 2012, Volume 15, Number 1, Pages 31–43 (Mi sjvm456)  

This article is cited in 7 scientific papers (total in 7 papers)

Numerical analysis of stochastic oscillators on supercomputers

S. S. Artemieva, A. A. Ivanovb, V. D. Korneevba

a Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University, Novosibirsk

Abstract: In this paper we investigate the numerical analysis problem of stochastic differential equations (SDEs) with oscillating solutions. The dependence of mathematical expectation and dispersion of the SDE numerical solution on the mesh size of integrating the generalized Euler method is determined. The results of numerical experiments with simulation of linear and nonlinear stochastic oscillators on the supercomputer of the Siberian Supercomputer Center are presented.

Key words: stochastic differential equations, statistical algorithms, parallelization, supercomputer, cluster, van der Pol equation, phase trajectory, stochastic oscillators.

Full text: PDF file (716 kB)
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English version:
Numerical Analysis and Applications, 2012, 5:1, 25–35

UDC: 519.676
Received: 28.06.2010
Revised: 28.02.2011

Citation: S. S. Artemiev, A. A. Ivanov, V. D. Korneev, “Numerical analysis of stochastic oscillators on supercomputers”, Sib. Zh. Vychisl. Mat., 15:1 (2012), 31–43; Num. Anal. Appl., 5:1 (2012), 25–35

Citation in format AMSBIB
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\by S.~S.~Artemiev, A.~A.~Ivanov, V.~D.~Korneev
\paper Numerical analysis of stochastic oscillators on supercomputers
\jour Sib. Zh. Vychisl. Mat.
\yr 2012
\vol 15
\issue 1
\pages 31--43
\mathnet{http://mi.mathnet.ru/sjvm456}
\elib{https://elibrary.ru/item.asp?id=17979264}
\transl
\jour Num. Anal. Appl.
\yr 2012
\vol 5
\issue 1
\pages 25--35
\crossref{https://doi.org/10.1134/S199542391201003X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84857888964}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. S. Artemiev, V. D. Korneev, M. A. Yakunin, “Numerical solution to stochastic differential equations with a random structure on supercomputers”, Num. Anal. Appl., 6:4 (2013), 261–267  mathnet  crossref  mathscinet  elib
    2. S. S. Artemiev, A. A. Ivanov, D. D. Smirnov, “New frequency characteristics of the numerical solution to stochastic differential equations”, Num. Anal. Appl., 8:1 (2015), 13–22  mathnet  crossref  mathscinet  elib
    3. S. S. Artemiev, A. A. Ivanov, “Analysis of the effect of random noise on the strange attractors of Monte Carlo on a supercomputer”, Num. Anal. Appl., 8:2 (2015), 101–112  mathnet  crossref  crossref  mathscinet  elib
    4. S. S. Artemiev, M. A. Yakunin, “Analysis of the accuracy of estimates of the first moments of solving SDE with Wiener and Poisson components by Monte Carlo method”, Num. Anal. Appl., 9:1 (2016), 24–33  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    5. S. S. Artemiev, A. A. Ivanov, “Analysis of the influence of random noises for self-oscillating chemical reactions by a Monte-Carlo method on supercomputers”, J. Appl. Industr. Math., 10:4 (2016), 468–473  mathnet  crossref  crossref  mathscinet  elib
    6. S. S. Artemiev, M. A. Yakunin, “Parametric analysis of the oscillatory solutions to SDEs with Wiener and Poisson components by a Monte Carlo method”, J. Appl. Industr. Math., 11:2 (2017), 157–167  mathnet  crossref  crossref  elib
    7. A. A. Ivanov, “Analysis of the stochastic motion of a charged particle in a magnetic field by the Monte Carlo method on supercomputers”, J. Appl. Industr. Math., 11:3 (2017), 362–368  mathnet  crossref  crossref  elib
  • Sibirskii Zhurnal Vychislitel'noi Matematiki
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