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SUMMARY:On the time discretization of kinetic equations in stiff regimes -
  Pareschi\, L (Ferrara)
DTSTART:20100910T090000Z
DTEND:20100910T100000Z
UID:TALK26075@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We review some results concerning the time discretization of k
 inetic equations in stiff regimes and their stability properties. Such pro
 perties are particularly important in applications involving several lengh
 t scales like in the numerical treatment of fluid-kinetic regions. We emph
 asize limitations presented by several standard schemes and focus our atte
 ntion on a class of exponential Runge-Kutta integration methods. Such meth
 ods are based on a decomposition of the collision operator into an equilib
 rium and a non equilibrium part and are exact for relaxation operators of 
 BGK type. For Boltzmann type kinetic equations they work uniformly for a w
 ide range of relaxation times and avoid the solution of nonlinear systems 
 of equations even in stiff regimes. We give sufficient conditions in order
  that such methods are unconditionally asymptotically stable and asymptoti
 c preserving. Such stability properties are essential to guarantee the cor
 rect asymptotic behavior for small relaxation times. The methods also offe
 r favorable properties such as nonnegativity of the solution and entropy i
 nequality. For this reason\, as we will show\, the methods are suitable bo
 th for deterministic as well as probabilistic numerical techniques.
LOCATION:Seminar Room 1\, Newton Institute
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