Skip to main content
SpringerLink
Log in

Application of stochastic equivalence for solving parabolic partial differential equations

  • Published:
Computational Mathematics and Mathematical Physics Aims and scope Submit manuscript

Abstract

An approach to solving parabolic partial differential equations based on the method of stochastic characteristics is proposed. The method allows decomposition of the numerical procedure into separate unified blocks. The approximation error and the efficiency of the method are evaluated. An example is given.

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. V. S. Pugachev and I. N. Sinitsyn, Stochastic Differential Systems (Nauka, Moscow, 1990) [in Russian].

    Google Scholar 

  2. H. J. Kushner, Probability Methods for Approximations in Stochastic Control and for Elliptic Equations (Academic, New York, 1977; Nauka, Moscow, 1985).

    Google Scholar 

  3. O. Hellman, Introduction to the Theory of Optimal Search (Nauka, Moscow, 1985) [in Russian].

    Google Scholar 

  4. V. V. Khutortsev, “Synthesis of the Optimal Control Of Continuous Markov Processes Using Semidefinite Objective Functionals,” Avtom. Telemekh., No. 1, 80–89 (2001).

  5. V. S. Vladimirov, Equations of Mathematical Physics (Nauka, Moscow, 1988) [in Russian].

    Google Scholar 

  6. N. V. Krylov and B. L. Rozovskii, “Stochastic Partial Differential Equations and Diffusion Processes,” Usp. Mat. Nauk 37(6), 75–95 (1982).

    MathSciNet  Google Scholar 

  7. B. L. Rozovskii, Evolution Stochastic Systems (Nauka, Moscow, 1983) [in Russian].

    Google Scholar 

  8. I. I. Gikhman and A. V. Skorokhod, Introduction to the Theory of Random Processes (Nauka, Moscow, 1977; Dover, Mineola, N.Y., 1996).

    Google Scholar 

  9. M. S. Yarlykov, Application of the Markov Theory of Nonlinear Filtration in Radio Engineering (Sovetskoe Radio, Moscow, 1980) [in Russian].

    Google Scholar 

  10. G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, New York, 1968; Nauka, Moscow, 1974).

    Google Scholar 

  11. I. V. Prangishvili, S. Ya. Vilenkin, and I. L. Medvedev, Parallel Computer Systems with Shared Control (Energoatomizdat, Moscow, 1983) [in Russian].

    Google Scholar 

  12. V. I. Tikhonov and V. N. Kharisov, Statistical Analysis and Synthesis in Radio Engineering (Radio i Svyaz’, Moscow, 1991) [in Russian].

    Google Scholar 

  13. V. N. Taran and V. V. Khutortsev, “Application of the Spline-Collocation Method for the Synthesis of a Detection and Evaluation System,” Probl. Peredachi Inf. 20(4), 41–50 (1984).

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Rostov Military Higher Engineering School of Missile Corps, Rostov-on-Don, 344027, Russia

    V. V. Khutortsev

Authors
  1. V. V. Khutortsev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © V.V. Khutortsev, 2006, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2006, Vol. 46, No. 3, pp. 421–432.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Khutortsev, V.V. Application of stochastic equivalence for solving parabolic partial differential equations. Comput. Math. and Math. Phys. 46, 402–412 (2006). https://doi.org/10.1134/S0965542506030079

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0965542506030079

Keywords

Search

Navigation