Talks and Poster Presentations (without Proceedings-Entry):

W. Auzinger, H. Hofstätter, T. Jawecki, O. Koch, K. Kropielnicka, P. Singh:
"Adaptive exponential methods";
Talk: SciCADE 2019, International Conference on Scientific Computation and Differential Equations, Innsbruck; 2019-07-22 - 2019-07-26.

English abstract:
We investigate exponential-based adaptive numerical time integrators for time-dependent systems of
linear ordinary differential equations of Schrödinger type. Applications in the study of the design of
novel solar cells motivate the interest in finding efficient adaptive time integration methods for this task.
We consider commutator-free Magnus-type methods, classical Magnus integrators and novel integrators
based on a splitting approach. In all the methods, efficient time-stepping is realized based on defectbased estimators for the local error constructed especially for the task. We show the asymptotical
correctness of the error estimators and demonstrate the advantages of adaptive time-stepping.

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