Type: Seminar

Distribution: World

Expiry: 12 Apr 2012

Auth: gottwald@101.161.37.120 in SMS-auth

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