W. Auzinger, H. Hofstätter, O. Koch, M. Quell, M. Thalhammer:
"A Posteriori Error Estimation for Magnus-Type Integrators";
ESAIM: Mathematical Modelling and Numerical Analysis, 53 (2019), 1; S. 197 - 218.

Kurzfassung englisch:
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 two numerical examples.

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