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TitleDefect-based local error estimators for splitting methods, with application to Schrödinger equations, Part III: The nonlinear case
Author(s) Winfried Auzinger, Harald Hofstätter, Othmar Koch, Mechthild Thalhammer
TypeArticle in Journal
AbstractAbstract 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.
KeywordsNonlinear evolution equations, Time-dependent nonlinear Schrödinger equations, Exponential operator splitting methods, A priori local error analysis, A posteriori local error analysis
URL http://www.sciencedirect.com/science/article/pii/S0377042714002854
JournalJournal of Computational and Applied Mathematics
Pages182 - 204
Translation No
Refereed No