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

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Monte Carlo methods for solving the first boundary value problem for a polyharmonic equation. / Lukinov, V. L.; Mikhailov, G. A.

In: Computational Mathematics and Mathematical Physics, Vol. 45, No. 3, 01.03.2005, p. 476-489.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{62910ee14f8a44b69549fea25f5e9b66,

title = "Monte Carlo methods for solving the first boundary value problem for a polyharmonic equation",

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.",

keywords = "{"}walk-by-spheres{"} algorithm, Dirichlet problem, Monte Carlo method, Polyharmonic equation, Random parameters",

author = "Lukinov, {V. L.} and Mikhailov, {G. A.}",

year = "2005",

month = mar,

day = "1",

language = "English",

volume = "45",

pages = "476--489",

journal = "Computational Mathematics and Mathematical Physics",

issn = "0965-5425",

publisher = "PLEIADES PUBLISHING INC",

number = "3",

}

RIS

TY - JOUR

T1 - Monte Carlo methods for solving the first boundary value problem for a polyharmonic equation

AU - Lukinov, V. L.

AU - Mikhailov, G. A.

PY - 2005/3/1

Y1 - 2005/3/1

N2 - 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.

AB - 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.

KW - "walk-by-spheres" algorithm

KW - Dirichlet problem

KW - Monte Carlo method

KW - Polyharmonic equation

KW - Random parameters

UR - http://www.scopus.com/inward/record.url?scp=33746538933&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=13483775

M3 - Article

AN - SCOPUS:33746538933

VL - 45

SP - 476

EP - 489

JO - Computational Mathematics and Mathematical Physics

JF - Computational Mathematics and Mathematical Physics

SN - 0965-5425

IS - 3

ER -

ID: 24442365