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W. Auzinger, H. Hofstätter, O. Koch, M. Quell, M. Thalhammer:
"A Posteriori Error Estimation for Magnus-Type Integrators";
in: "ASC Report 1/2018", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2018, ISBN: 978-3-902627-11-7, 1 - 19.

We study high-order Magnus-type exponential integrators for large systems of ordinary di˙erential equations defined by a time-dependent skew-Hermitian matrix. We construct and analyze defect-based local error estimators as the basis for adaptive stepsize selection. The resulting procedures provide a posteriori information on the local error and hence enable the accurate, efficient, and reliable time integration of the model equations. The theoretical results are illustrated on a model of solar cells composed of heterostructures based on transition metal oxides.

http://www.asc.tuwien.ac.at/preprint/2018/asc01x2018.pdf