Skip to main content
SpringerLink
Log in

Weighted Monte Carlo Methods for Approximate Solution of a Nonlinear Boltzmann Equation

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

Abstract

We construct weighted modifications of statistical modeling of an ensemble of interacting particles which is connected with approximate solution of a nonlinear Boltzmann equation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bird G. A., Molecular Gas Dynamics [Russian translation], Mir, Moscow (1981).

    Google Scholar 

  2. Rogazinskii S. V., “One approach to solving the homogeneous Boltzmann equation,” Zh. Vychisl. Mat. i Mat. Fiz., 27, No. 4, 564–574 (1987).

    Google Scholar 

  3. Korolëv A. E. and Yanitskii V. E., “Direct statistical modeling of the collision relaxation for gas mixtures with large discrepancy in concentrations,” Zh. Vychisl. Mat. i Mat. Fiz., 23, No. 3, 674–680 (1983).

    Google Scholar 

  4. Mikhailov G. A., Parametric Estimates by the Monte Carlo Method, VSP, Utrecht (1999).

    Google Scholar 

  5. Mikhailov G. A., Weighted Monte Carlo Methods [in Russian], Izdat. Sibirsk. Otdel. Ros. Akad. Nauk, Novosibirsk (2000).

    Google Scholar 

  6. Ivanov M. S. and Rogazinskii S. V., “Economical schemes for statistical modeling of ows of a rarefied gas,” Mat. Model., 1, No. 7, 130–145 (1989).

    Google Scholar 

  7. Leontovich M. A., “Principal equations of kinetic gas theory from the viewpoint of the theory of stochastic processes,” Zh. Éksper. Teoret. Fiz., 5, 211 (1935).

    Google Scholar 

  8. Povzner A. Ya., “On the Boltzmann equation of kinetic gas theory,” Mat. Sb., 58, 65–86 (1962).

    Google Scholar 

  9. Kac M., Probability and Related Topics in Physical Sciences [Russian translation], Mir, Moscow (1965).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The Institute of Computer Mathematics and Mathematical Geophysics, Novosibirsk

    G. A. Mikhailov & S. V. Rogazinskii

Authors
  1. G. A. Mikhailov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. V. Rogazinskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mikhailov, G.A., Rogazinskii, S.V. Weighted Monte Carlo Methods for Approximate Solution of a Nonlinear Boltzmann Equation. Siberian Mathematical Journal 43, 496–503 (2002). https://doi.org/10.1023/A:1015467719806

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1015467719806

Search

Navigation