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Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 4, Pages 715–726 (Mi zvmmf490)  

This article is cited in 8 scientific papers (total in 8 papers)

Weighted Monte Carlo method for an approximate solution of the nonlinear coagulation equation

G. A. Mikhailov, S. V. Rogazinskii, N. M. Ureva

Institute of Computational Mathematics and Mathematical Geophysics, Siberian Division, Russian Academy of Sciences, Novosibirsk, pr. Akademika Lavrent'eva 6, 630090, Russia

Abstract: New weighted modifications of direct statistical simulation methods designed for the approximate solution of the nonlinear Smoluchowski equation are developed on the basis of stratification of the interaction distribution in a multiparticle system according to the index of a pair of interacting particles. The weighted algorithms are validated for a model problem with a known solution. It is shown that they effectively estimate variations in the functionals with varying parameters, in particular, with the initial number $N_0$ of particles in the simulating ensemble. The computations performed for the problem with a known solution confirm the semiheuristic hypothesis that the model error is $O(N_0^{-1})$. Estimates are derived for the derivatives of the approximate solution with respect to the coagulation coefficient.

Key words: Smoluchowski equation, Monte Carlo method, numerical algorithm.

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English version:
Computational Mathematics and Mathematical Physics, 2006, 46:4, 680–690

Bibliographic databases:

UDC: 519.633
Received: 07.11.2005

Citation: G. A. Mikhailov, S. V. Rogazinskii, N. M. Ureva, “Weighted Monte Carlo method for an approximate solution of the nonlinear coagulation equation”, Zh. Vychisl. Mat. Mat. Fiz., 46:4 (2006), 715–726; Comput. Math. Math. Phys., 46:4 (2006), 680–690

Citation in format AMSBIB
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\paper Weighted Monte Carlo method for an approximate solution of the nonlinear coagulation equation
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 4
\pages 715--726
\mathnet{http://mi.mathnet.ru/zvmmf490}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2260359}
\zmath{https://zbmath.org/?q=an:05200938}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 4
\pages 680--690
\crossref{https://doi.org/10.1134/S0965542506040130}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746050310}


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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. M. A. Korotchenko, G. A. Mikhailov, S. V. Rogazinskii, “Modifications of weighted Monte Carlo algorithms for nonlinear kinetic equations”, Comput. Math. Math. Phys., 47:12 (2007), 2023–2033  mathnet  crossref  mathscinet
    2. Mikhailov R.G.A., Korotchenko M.A., Rogasinsky S.V., “Importance modeling algorithms for solving nonlinear kinetic equations”, Dokl. Math., 76:1 (2007), 502–505  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    3. Korotchenk M.A., Mikhailov G.A., Rogazinskii S.V., “Value modifications of weighted statistical modelling for solving nonlinear kinetic equations”, Russian J. Numer. Anal. Math. Modelling, 22:5 (2007), 471–486  crossref  mathscinet  zmath  isi  scopus
    4. Marchenko M.A., “A study of a parallel statistical modelling algorithm for solution of the nonlinear coagulation equation”, Russian J. Numer. Anal. Math. Modelling, 23:6 (2008), 597–613  crossref  mathscinet  zmath  isi  elib  scopus
    5. Rogasinsky S.V., “Statistical modelling of the solution of the nonlinear Boltzmann equation in the spatially inhomogeneous case”, Russian J. Numer. Anal. Math. Modelling, 24:5 (2009), 495–513  crossref  mathscinet  zmath  isi  elib  scopus
    6. Mikhailov G.A. Rogazinskii S.V., “The Modified Majorant Frequency Method for Numerical Simulation of the Generalized Exponential Distribution”, Dokl. Math., 85:3 (2012), 325–327  crossref  mathscinet  zmath  isi  elib  elib  scopus
    7. Mikhailov G.A. Rogazinskii S.V., “Probabilistic Model of Many-Particle Evolution and Estimation of Solutions to a Nonlinear Kinetic Equation”, Russ. J. Numer. Anal. Math. Model, 27:3 (2012), 229–242  crossref  mathscinet  zmath  isi  elib  scopus
    8. A. V. Burmistrov, M. A. Korotchenko, “Weight Monte Carlo algorithms for estimation and parametric analysis of the solution to the kinetic coagulation equation”, Num. Anal. Appl., 7:2 (2014), 104–116  mathnet  crossref  mathscinet  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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