Time integration methods for non-autonomous evolution equations
- Referent: Prof. Dr. Mechthild Thalhammer
- Ort: Seminarraum 1.067, Gebäude 20.30
- Termin: 9.2.2017, 14:00 - 15:00 Uhr
- Gastgeber: SFB 1173
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 or diffusion-reaction systems with additional multiplicative noise modelling pattern formation.