Probabilistic representation and Monte Carlo methods for the first boundary value problem for a polyharmonic equation

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Abstract

In this paper we give the results obtained by the constructed probabilistic representation of the solution to the first boundary value problem for a polyharmonic equation. It is shown that this solution is expressed by the parametric derivative of the solution to the specially constructed Dirichlet problem for the Helmholtz equation. On this basis we develop new algorithms of 'walk on a grid' and 'random walk by spheres' for the solution of a polyharmonic equation.

Original languageEnglish
Pages (from-to)433-448
Number of pages16
JournalRussian Journal of Numerical Analysis and Mathematical Modelling
Volume19
Issue number5
DOIs
Publication statusPublished - 2004
Externally publishedYes

State classification of scientific and technological information

  • 27.41 Computational mathematics

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