SMS scnews item created by Georg Gottwald at Thu 5 Apr 2012 0901
Type: Seminar
Distribution: World
Expiry: 12 Apr 2012
Calendar1: 10 Apr 2012 1500-1600
CalLoc1: Carslaw 451
Auth: gottwald@101.161.37.120 in SMS-auth

# SDG meeting: Arieh Iserles -- Splittings, commutators and the linear Schrödinger equation

Next week, Tuesday the 10th of April, Arieh Iserles (Cambridge) will give a talk at USyd
Carslaw 451 at 3pm on

"Splittings, commutators and the linear Schrödinger equation"

Abstract: In this talk I report recent work on the discretization of the linear
Schrödinger equation by exponential splitting in a manner that separates different
scales of frequency.  Working at the level of differential operators, it is possible to
represent the solution, using symmetric Zassenhaus splitting and free Lie algebras, as a
product of exponentials, so that the argument of each exponential is of a different
order of magnitude: in effect, we have an asymptotic expansion in powers of the small
parameter.  Then, and only then, we replace derivatives by differentiation matrices.
However, this requires substantial effort to conserve unitarity.  The standard approach
of spectral methods does not work but, using generalised polar decomposition, we show
that both pseudospectral methods and spectral collocation are equal to the task.

(Note the unusual date and time!)

Hope to see you all,

Georg


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