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Monte Carlo Solution of Dirichlet Problem for Semi-linear Equation

  • Abdujabbor RasulovEmail author
  • Gulnora Raimova
  • Matyokub Bakoev
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11386)

Abstract

In the present work Dirichlet boundary value problem (BVR) for semi-linear elliptic equation is considered. Assuming the existence of solution BVR obtained a probabilistic representation of the solution as a mathematical expectation of some random variable. In accordance with a probabilistic representation on the trajectories of the branching random process were constructed unbiased estimator of the solution. An unbiased estimator of the solution has finite variance, based on the trajectories of a branching process with a finite average number of branching and easily simulated. Some numerical experiments are performed.

Keywords

Monte Carlo method An unbiased estimator Branching random process Markov chain Dirichlet problem 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Abdujabbor Rasulov
    • 1
    Email author
  • Gulnora Raimova
    • 2
  • Matyokub Bakoev
    • 1
  1. 1.University of World Economy and DiplomacyTashkentUzbekistan
  2. 2.Institute of Mathematics, Academy of SciencesTashkentUzbekistan

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