Splittings, commutators and the linear Schrödinger equation

Host Institution:

La Trobe University

Title of Seminar:

Splittings, commutators and the linear Schrödinger equation

Speaker's Name:

Prof Arieh Iserles

Speaker's Institution:

University of Cambridge, UK

Time and Date:

Friday 30 March, 2012, 2:00pm (AEDT)

Seminar Abstract:

In this talk I report  recent work, joint with Karolina Kropielnicka, on the solution of the linear Schrödinger equation by exponential splitting in a manner that separates different scales of frequency. I demonstrate that, contrary to expectations, once the equation is discretized appropriately, the size of iterated commutators becomes very small: appropriate discretizations include finite difference and spectral collocation methods, but not the standard spectral method usually employed in this context. This rapid decay in the size of commutators allows us to use high-order symmetric Zassenhaus splittings which separate frequencies very well and allow large time steps. The talk will bring together themes in PDEs, numerical analysis, free Lie algebras and even some approximation theory.

Seminar Convenor:

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