| Issue |
ESAIM: M2AN
Volume 53, Number 1, January–February 2019
|
|
|---|---|---|
| Page(s) | 197 - 218 | |
| DOI | https://doi.org/10.1051/m2an/2018050 | |
| Published online | 10 April 2019 | |
A posteriori error estimation for Magnus-type integrators
1
Technische Universität Wien, Institut für Analysis und Scientific Computing, Wiedner Hauptstraße 8-10, 1040 Wien, Austria
2
Universität Wien, Fakultät für Mathematik, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria
3
Leopold-Franzens Universität Innsbruck, Institut für Mathematik, Technikerstraße 13, 6020 Innsbruck, Austria
* Corresponding author: othmar@othmar-koch.org
Received:
20
December
2017
Accepted:
25
August
2018
We study high-order Magnus-type exponential integrators for large systems of ordinary differential 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 .
Mathematics Subject Classification: 65L05 / 65L20 / 65L50 / 65L70
Key words: Non-autonomous linear differential equations / magnus-type integrators / a posteriori local error estimation / asymptotical correctness / adaptive stepsize selection
© EDP Sciences, SMAI 2019
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