Two variants of Monte Carlo projection method for numerical solution of nonlinear Boltzmann equation

Sergey V. Rogasinsky

doi:10.1515/rnam-2019-0012

Two variants of Monte Carlo projection method for numerical solution of nonlinear Boltzmann equation

Sergey V. Rogasinsky

Кафедра вычислительной математики ММФ

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

Аннотация

The paper is focused on justification of a statistical modelling algorithm for solution of the nonlinear kinetic Boltzmann equation on the base of a projection method. Hermite functions are used as an orthonormal basis. The error of approximation of a function by a partial sum of Hermite functions series is estimated in the L₂ norm. The estimates are compared for two variants of the projection method in the case of solutions to the homogeneous gas relaxation problem with a known solution.

Язык оригинала	английский
Страницы (с-по)	143-150
Число страниц	8
Журнал	Russian Journal of Numerical Analysis and Mathematical Modelling
Том	34
Номер выпуска	3
DOI	https://doi.org/10.1515/rnam-2019-0012
Состояние	Опубликовано - 1 июн 2019

Доступ к документу

10.1515/rnam-2019-0012

Link to publication in Scopus

Fingerprint Подробные сведения о темах исследования «Two variants of Monte Carlo projection method for numerical solution of nonlinear Boltzmann equation». Вместе они формируют уникальный семантический отпечаток (fingerprint).

Цитировать

@article{3c9e0ac7e65c443eb626145242d1d62f,

title = "Two variants of Monte Carlo projection method for numerical solution of nonlinear Boltzmann equation",

abstract = "The paper is focused on justification of a statistical modelling algorithm for solution of the nonlinear kinetic Boltzmann equation on the base of a projection method. Hermite functions are used as an orthonormal basis. The error of approximation of a function by a partial sum of Hermite functions series is estimated in the L2 norm. The estimates are compared for two variants of the projection method in the case of solutions to the homogeneous gas relaxation problem with a known solution.",

keywords = "Hermite polynomials, Monte Carlo method, nonlinear Boltzmann equation, Projection method",

author = "Rogasinsky, {Sergey V.}",

year = "2019",

month = jun,

day = "1",

doi = "10.1515/rnam-2019-0012",

language = "English",

volume = "34",

pages = "143--150",

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

issn = "0927-6467",

publisher = "Walter de Gruyter GmbH",

number = "3",

}

Two variants of Monte Carlo projection method for numerical solution of nonlinear Boltzmann equation. / Rogasinsky, Sergey V.

В: Russian Journal of Numerical Analysis and Mathematical Modelling, Том 34, № 3, 01.06.2019, стр. 143-150.

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

TY - JOUR

T1 - Two variants of Monte Carlo projection method for numerical solution of nonlinear Boltzmann equation

AU - Rogasinsky, Sergey V.

PY - 2019/6/1

Y1 - 2019/6/1

N2 - The paper is focused on justification of a statistical modelling algorithm for solution of the nonlinear kinetic Boltzmann equation on the base of a projection method. Hermite functions are used as an orthonormal basis. The error of approximation of a function by a partial sum of Hermite functions series is estimated in the L2 norm. The estimates are compared for two variants of the projection method in the case of solutions to the homogeneous gas relaxation problem with a known solution.

AB - The paper is focused on justification of a statistical modelling algorithm for solution of the nonlinear kinetic Boltzmann equation on the base of a projection method. Hermite functions are used as an orthonormal basis. The error of approximation of a function by a partial sum of Hermite functions series is estimated in the L2 norm. The estimates are compared for two variants of the projection method in the case of solutions to the homogeneous gas relaxation problem with a known solution.

KW - Hermite polynomials

KW - Monte Carlo method

KW - nonlinear Boltzmann equation

KW - Projection method

UR - http://www.scopus.com/inward/record.url?scp=85067429648&partnerID=8YFLogxK

U2 - 10.1515/rnam-2019-0012

DO - 10.1515/rnam-2019-0012

M3 - Article

AN - SCOPUS:85067429648

VL - 34

SP - 143

EP - 150

JO - Russian Journal of Numerical Analysis and Mathematical Modelling

JF - Russian Journal of Numerical Analysis and Mathematical Modelling

SN - 0927-6467

IS - 3

ER -