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

VL Lukinov; GA Mikhailov

doi:10.1163/1569398042395989

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

Результат исследования: Научные публикации в периодических изданиях › статья › рецензирование

Аннотация

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.

Язык оригинала	английский
Страницы (с-по)	433-448
Число страниц	16
Журнал	Russian Journal of Numerical Analysis and Mathematical Modelling
Том	19
Номер выпуска	5
DOI	https://doi.org/10.1163/1569398042395989
Состояние	Опубликовано - 2004
Опубликовано для внешнего пользования	Да

ГРНТИ

27.41 Вычислительная математика

Доступ к документу

10.1163/1569398042395989

Другие файлы и ссылки

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

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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.",

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

В: Russian Journal of Numerical Analysis and Mathematical Modelling, Том 19, № 5, 2004, стр. 433-448.

Результат исследования: Научные публикации в периодических изданиях › статья › рецензирование

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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.

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JF - Russian Journal of Numerical Analysis and Mathematical Modelling

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