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

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Probabilistic representation and Monte Carlo methods for the first boundary value problem for a polyharmonic equation. / Lukinov, VL ; Mikhailov, GA.

In: Russian Journal of Numerical Analysis and Mathematical Modelling, Vol. 19, No. 5, 2004, p. 433-448.

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

BibTeX

@article{c66b5fd8ba6c43478820dd76556e5d86,

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

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.",

author = "VL Lukinov and GA Mikhailov",

year = "2004",

doi = "10.1163/1569398042395989",

language = "English",

volume = "19",

pages = "433--448",

journal = "Russian Journal of Numerical Analysis and Mathematical Modelling",

issn = "0927-6467",

publisher = "Walter de Gruyter GmbH",

number = "5",

}

RIS

TY - JOUR

T1 - Probabilistic representation and Monte Carlo methods for the first boundary value problem for a polyharmonic equation

AU - Lukinov, VL

AU - Mikhailov, GA

PY - 2004

Y1 - 2004

N2 - 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.

AB - 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.

UR - https://www.elibrary.ru/item.asp?id=13460448

U2 - 10.1163/1569398042395989

DO - 10.1163/1569398042395989

M3 - Article

VL - 19

SP - 433

EP - 448

JO - Russian Journal of Numerical Analysis and Mathematical Modelling

JF - Russian Journal of Numerical Analysis and Mathematical Modelling

SN - 0927-6467

IS - 5

ER -

ID: 24441905