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Monte Carlo Solution of Dirichlet Problem for Semi-linear Equation

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Finite Difference Methods. Theory and Applications (FDM 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11386))

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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.

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Author information

Authors and Affiliations

  1. University of World Economy and Diplomacy, Tashkent, Uzbekistan

    Abdujabbor Rasulov & Matyokub Bakoev

  2. Institute of Mathematics, Academy of Sciences, Tashkent, Uzbekistan

    Gulnora Raimova

Authors
  1. Abdujabbor Rasulov
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  2. Gulnora Raimova
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  3. Matyokub Bakoev
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Corresponding author

Correspondence to Abdujabbor Rasulov .

Editor information

Editors and Affiliations

  1. IICT, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Dimov

  2. Eötvös Loránd University, Budapest, Hungary

    István Faragó

  3. University of Rousse, Rousse, Bulgaria

    Lubin Vulkov

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Rasulov, A., Raimova, G., Bakoev, M. (2019). Monte Carlo Solution of Dirichlet Problem for Semi-linear Equation. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Finite Difference Methods. Theory and Applications. FDM 2018. Lecture Notes in Computer Science(), vol 11386. Springer, Cham. https://doi.org/10.1007/978-3-030-11539-5_51

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  • DOI: https://doi.org/10.1007/978-3-030-11539-5_51

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-11538-8

  • Online ISBN: 978-3-030-11539-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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