Numerical study of a stochastic weighted particle method for a model kinetic equation
type: Item
instance of: scholarly article
title: Numerical study of a stochastic weighted particle method for a model kinetic equation
zbMATH Open document ID: 0862.65092
author: S. Rjasanow
author: Wolfgang Wagner
published in: Journal of Computational Physics
publication date: 1996-12-19T00:00:00Z
review text: The paper continues the study of a new partial method for nonlinear kinetic equations introduced by the authors [J. Comput. Phys. 124, No. 2, 243-253, Art. No. 0057 (1996)]. The method is based on a generalized procedure of modelling collisions between particles providing some freedom in the random choice of the collision partners. Earlier the existence of the solution of the kinetic model equation, the stability of the solution, and the convergence of a class of difference schemes was studied. The solution can be expressed as sum of a complex Fourier series and belongs to the space \(L^2(0,1)\). The stochastic weighted particle method presented in this paper consists in modelling trajectories of a stochastic particle system. The main feature of the method is the presence of certain control parameters giving the opportunity to adapt the behavior of the particle system to specific numerical purposes. It is shown that the numbers of particles with prescribed velocities may be artificially increased by the new method. The computations were performed for a model kinetic equation, for which the exact solution is known. The results obtained give us recommendations for mode complicated kinetic equations like the Boltzmann equation.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 60H30
Mathematics Subject Classification ID: 82C40
zbMATH DE Number: 947687
zbMATH Keywords: nonlinear integral equations
zbMATH Keywords: nonlinear kinetic equations
zbMATH Keywords: stochastic weighted particle method
zbMATH Keywords: Boltzmann equation
reviewed by: Iulian Coroian
MaRDI profile type: Publication
full work available at URL: jcph.1996.0216
OpenAlex ID: W2065489267
DOI: 10.1006/JCPH.1996.0216
description: scientific article; zbMATH DE number 947687