NDLI: On the Approximation of the Vlasov--Poisson System by Particle Methods

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Wollman, Stephen
Copyright Year	2000
Abstract	A discrete approximation to the Vlasov--Poisson system is given which can be viewed as a type of particle method. Approximations to the characteristic curves are computed and proved to converge in a strict sense to the exact trajectories of the system. In particular it is shown that the particle method converges for a general nonuniform distribution of initial aproximating points. Two theorems are proved. In the first theorem it is shown that in theory a convergence of the method can be obtained with mollification of the approximate electric field which is on the order of the interparticle distance. However, the mollifier in this case is not of a form that is of practical use in computation. In the second theorem it is proved that the method converges for a simple mollifier that could be used in computation and which approaches zero at a slower rate than the interparticle distance.
Starting Page	1369
Ending Page	1398
Page Count	30
File Format	PDF
ISSN	00361429
DOI	10.1137/S0036142999298528
e-ISSN	10957170
Issue Number	4
Volume Number	37
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-25
Access Restriction	Subscribed
Subject Keyword	Stability and convergence of numerical methods Plasmas particle method proof of convergence Vlasov--Poisson system
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Numerical Analysis Computational Mathematics

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