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

Computational Mathematics Section

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

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.

Original language	English
Pages (from-to)	143-150
Number of pages	8
Journal	Russian Journal of Numerical Analysis and Mathematical Modelling
Volume	34
Issue number	3
DOIs	https://doi.org/10.1515/rnam-2019-0012
Publication status	Published - 1 Jun 2019

Keywords

Hermite polynomials
Monte Carlo method
nonlinear Boltzmann equation
Projection method

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10.1515/rnam-2019-0012

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