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Matem. Mod., 2007, Volume 19, Number 12, Pages 52–62 (Mi mm1226)  

This article is cited in 2 scientific papers (total in 2 papers)

Evolutionary algorithms of solution to boundary value problems in domains admitting decomposition

A. N. Vasilyev, D. A. Tarkhov

Saint-Petersburg State Polytechnical University

Abstract: Neural networks are considered as an effective and powerful tool for numerical solution of boundary value problems for partial differential equations. In this paper we focus our attention on the case of elliptic equations and domains admitting decomposition. The approximation of Dirichlet problem solution for the Laplace equation in complicated domain by means of neural networks is considered. Some original neural network training algorithms based on ideas of evolution modeling are offered. These algorithms allow some effective parallelization and generalization on similar problems.

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Received: 18.12.2006

Citation: A. N. Vasilyev, D. A. Tarkhov, “Evolutionary algorithms of solution to boundary value problems in domains admitting decomposition”, Matem. Mod., 19:12 (2007), 52–62

Citation in format AMSBIB
\Bibitem{VasTar07}
\by A.~N.~Vasilyev, D.~A.~Tarkhov
\paper Evolutionary algorithms of solution to boundary value problems in domains admitting decomposition
\jour Matem. Mod.
\yr 2007
\vol 19
\issue 12
\pages 52--62
\mathnet{http://mi.mathnet.ru/mm1226}
\zmath{https://zbmath.org/?q=an:1140.65354}


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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. A. N. Vasilev, “Matematicheskoe modelirovanie raspredelennykh sistem s pomoschyu neironnykh setei”, Matem. modelirovanie, 19:12 (2007), 32–42  mathnet  zmath
    2. Vasilev A.N., Tarkhov D.A., “Parametricheskie neirosetevye modeli klassicheskikh i neklassicheskikh zadach dlya uravneniya teploprovodnosti”, Nauchno-tekhnicheskie vedomosti SPbGPU, 2012, no. 153, 136–144  elib
  • Математическое моделирование
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