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SUMMARY:Computing the Schrödinger equation with no fear of commutators - 
 Arieh Iserles (DAMTP\, University of Cambridge)
DTSTART:20121011T140000Z
DTEND:20121011T150000Z
UID:TALK39865@talks.cam.ac.uk
CONTACT:Carola-Bibiane Schoenlieb
DESCRIPTION:In this talk I report  recent work on the solution of the line
 ar Schrödinger equation (LSE) by exponential splitting in a manner that s
 eparates different frequency scales. The main problem in discretizing LSE 
 is the presence of a very small parameter\, which generates exceedingly ra
 pid oscillation in the solution. However\, it is possible to exploit the f
 eatures of the graded free Lie algebra spanned by the Laplacian and by mul
 tiplication with the interaction potential to split the evolution operator
  in a symmetric Zassenhaus splitting so that the arguments of consecutive 
 exponentials constitute an asymptotic expansion in the small parameter. On
 ce we replace the Laplacian by an appropriate differentiation matrix\, thi
 s results in a high-order algorithm whose computational cost scales like O
 (N log N)\, where N is the number of degrees of freedom and whose error is
  uniform in the small parameter.
LOCATION:MR 14\, CMS
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