On the stability of spectral methods for the homogeneous Boltzmann equation

Authors
Pareschi, L Russo, G
Citation
L. Pareschi et G. Russo, On the stability of spectral methods for the homogeneous Boltzmann equation, TRANSP THEO, 29(3-5), 2000, pp. 431-447
Citations number
18
Categorie Soggetti
Physics
Journal title
TRANSPORT THEORY AND STATISTICAL PHYSICS
ISSN journal
00411450 → ACNP
Volume
29
Issue
3-5
Year of publication
2000
Pages
431 - 447
Database
ISI
SICI code
0041-1450(2000)29:3-5<431:OTSOSM>2.0.ZU;2-S
Abstract
In this paper we introduce a new smoothed scheme derived from the spectral Fourier method for the homogeneous Boltzmann equation recently introduced i n [14,15]. More precisely we show that using suitable smoothing filters the method can be designed in such a way that the spectral solution remains po sitive in time and preserves the total mass. Several numerical examples are given to illustrate the previous analysis.