Monte Carlo methods for solving the first boundary value problem for a polyharmonic equation

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

Results of solving the first boundary value problem for a polyharmonic equation are presented. The technique is based on the probabilistic representation of the solution of this problem constructed by the authors. Such a solution is shown to be a parametric derivative of the solution of a special Dirichlet problem for the Helmholtz equation. Based on this fact, new "walk-by-spheres" algorithms for a polyharmonic equation are developed. This made it possible to construct an algorithm implementing the Monte Carlo method for estimating the covariance function of the solution of a biharmonic equation with random functional parameters.

Original languageEnglish
Pages (from-to)476-489
Number of pages14
JournalComputational Mathematics and Mathematical Physics
Volume45
Issue number3
Publication statusPublished - 1 Mar 2005
Externally publishedYes

Keywords

  • "walk-by-spheres" algorithm
  • Dirichlet problem
  • Monte Carlo method
  • Polyharmonic equation
  • Random parameters

State classification of scientific and technological information

  • 27.41 Computational mathematics

Fingerprint Dive into the research topics of 'Monte Carlo methods for solving the first boundary value problem for a polyharmonic equation'. Together they form a unique fingerprint.

Cite this