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W. Auzinger, H. Hofstätter, O. Koch, M. Quell, M. Thalhammer:
"Adaptive Integrators for Schrödinger-Type Equations";
Talk: Workshop on modern numerical methods in quantum dynamics, Warschau (invited); 2017-03-20 - 2017-03-22.

We give an overview on recent work on a posteriori error estimation
for the purpose of time-adaptive integration of evolution equations of
Schrödinger type. In particular, splitting techniques are considered.
Depending on the problem at hand and the underlying scheme,
different techniques can be used. These include optimized embedded
pairs of schemes, the use of the adjoint of an (optimized) scheme,
and defect-based local error estimators. We concentrate on
the construction and efficient implementation of such error estimators
and present some examples, including ongoing work on
Magnus-type integrators for the case of time-dependent Hamiltonians.