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SUMMARY:Uniformly accurate numerical schemes for highly oscillatory kineti
 c and Schrödinger equations  - Mohammed Lemou (CNRS - University Rennes) 
DTSTART:20130618T104000Z
DTEND:20130618T113000Z
UID:TALK45881@talks.cam.ac.uk
CONTACT:HoD Secretary\, DPMMS
DESCRIPTION:This work is devoted to the construction of efficient numerica
 l schemes for a wide class of highly oscillatory models including kinetic 
 Vlasov models\, nonlinear Schr ödinger and Klein-Gordon equations. We pre
 sent a general strategy to construct numerical schemes which are uniformly
  accurate with respect to the oscillation frequency. This is a stronger fu
 ture than the usual so called "Asymptotic preserving" property\, the last 
 being therefore satisfied by our scheme in the highly oscillatory limit. O
 ur strategy enables to simulate the oscillatory problem without using any 
 mesh or time step refinement\, and the order of the scheme is preserved un
 iformly in all regimes. The method is based on a "double-scale" reformulat
 ion of the original equation\, with the introduction of an additional vari
 able. Then a link is made with well-known strategies based on Chapman-Ensk
 og expansions in kinetic theory\, which we extend to the dispersive contex
 t of Schrödinger-type equations. 
LOCATION:MR12
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