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SUMMARY:Splitting and Cayley-splitting integrators for Schödinger equatio
 ns - Sergio Blanes (Universidad Politécnica de Valencia)
DTSTART:20250605T140000Z
DTEND:20250605T150000Z
UID:TALK227740@talks.cam.ac.uk
CONTACT:Georg Maierhofer
DESCRIPTION:We consider the numerical integration of semi-discretised Schr
 ödinger equations requiring the computation of the exponential of a (skew
 -)Hermitian matrix acting on a vector. This is usually achieved by polynom
 ial methods such as Taylor\, Krylov or Chebyshev\, which are conditionally
  stable. However\, the skew-Hermitian matrix is usually separable into sol
 vable parts\, and tailored splitting methods can be used which preserve un
 itarity and they are unconditionally stable. In addition\, their accuracy 
 does not seem to deteriorate when considering a finer mesh\, unlike polyno
 mial methods. However\, resonances may appear. We analyse where resonances
  come from and how to reduce their undesirable effects. As an alternative\
 , we also analyse Cayley-splitting methods: they are unitary (unconditiona
 lly stable) methods\, they can avoid the resonances and\, in many cases\, 
 they are considerably cheaper to compute than the exponential splitting me
 thods. Some numerical examples will illustrate the potential interest of t
 he splitting methods as well as the new family of Cayley-splitting methods
 .
LOCATION:Centre for Mathematical Sciences\, MR14
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