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Contributions to Books:

W. Auzinger, H. Hofstätter, O. Koch, M. Thalhammer:
"Defect-based local error estimators for splitting methods, with application to Schrödinger equations Part III. The nonlinear case";
in: "ASC Report 19/2013", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2013, ISBN: 978-3-902627-06-3, 1 - 44.



English abstract:
The present work is concerned with the efficient time integration of nonlinear evolution equations by exponential operator splitting methods. Defect-based local error estimators serving as a reliable basis for adaptive stepsize control are constructed and analyzed. In the context of time-dependent nonlinear Schrödinger equations, asymptotical correctness of the local error estimators
associated with the first-order Lie-Trotter and second-order Strang splitting methods is proven. Numerical examples confirm the theoretical results and illustrate the performance of adaptive stepsize control.

Keywords:
The present work is concerned with the efficient time integration of nonlinear evolution equations by exponential operator splitting methods. Defect-based local error estimators serving as a reliable basis for adaptive stepsize control are constructed and


Electronic version of the publication:
http://www.asc.tuwien.ac.at/preprint/2013/asc19x2013.pdf



Related Projects:
Project Head Othmar Koch:
Adaptives Splitting für nichtlineare Schrödingergleichungen


Created from the Publication Database of the Vienna University of Technology.