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Efficient time integrators for non-autonomous linear and nonlinear Schrödinger equations

Presented by: 
Mechthild Thalhammer Leopold-Franzens Universtät Innsbruck
Date: 
Wednesday 10th July 2019 - 11:30 to 12:30
Venue: 
INI Seminar Room 1
Abstract: 
In this talk, I shall introduce the class of commutator-free quasi-Magnus exponential integrators for non-autonomous linear evolution equations and identify different areas of application.   Commutator-free quasi-Magnus exponential integrators are (formally) given by a composition of several exponentials that comprise certain linear combinations of the values of the defining operator at specified nodes. Avoiding the costly evaluation of commutators, they provide a favourable alternative to standard Magnus integrators, in particular for large-scale applications.   Non-autonomous linear evolution equations also arise as a part of more complex problems, for instance in connection with nonlinear evolution equations of the form u'(t) = A(t) u(t) + B(u(t)). A natural approach is thus to apply operator splitting methods combined with commutator-free quasi-Magnus exponential integrators. Relevant applications include Schrödinger equations with space-time-dependent potential describing Bose-Einstein condensation.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons