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Zapiski Nauchnykh Seminarov POMI, 2015, Volume 442, Pages 133–142 (Mi znsl6249)  
This article is cited in 1 scientific paper (total in 1 paper)

On stochastic algorithms for solving boundary value problems for the Laplace operator

A. S. Sipin

Vologda State University, Vologda, Russia
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Abstract: The paper deals with the mixed boundary value problem for the Poisson equation. A random walk inside the domain are constructed and unbiased estimator for the solution of the boundary value problem defined on its trajectories. The finiteness of the estimator variance proved. The possibility of practical realization of the estimator by Monte Carlo method studied.
Key words and phrases: unbiased estimator, boundary value problems, Laplace operator, Monte Carlo method.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00271
15-01-01698
Received: 07.12.2015
English version:
Journal of Mathematical Sciences (New York), 2017, Volume 225, Issue 5, Pages 812–817
DOI: https://doi.org/10.1007/s10958-017-3497-y
Bibliographic databases:
Document Type: Article
UDC: 519.2
Language: Russian
Citation: A. S. Sipin, “On stochastic algorithms for solving boundary value problems for the Laplace operator”, Probability and statistics. Part 23, Zap. Nauchn. Sem. POMI, 442, POMI, St. Petersburg, 2015, 133–142; J. Math. Sci. (N. Y.), 225:5 (2017), 812–817
Citation in format AMSBIB
\Bibitem{Sip15}
\by A.~S.~Sipin
\paper On stochastic algorithms for solving boundary value problems for the Laplace operator
\inbook Probability and statistics. Part~23
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 442
\pages 133--142
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6249}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3506850}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2017
\vol 225
\issue 5
\pages 812--817
\crossref{https://doi.org/10.1007/s10958-017-3497-y}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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