Auzinger, W., Hofstätter, H., Koch, O., & Thalhammer, M. (2015). Defect-based local error estimators for splitting methods, with application to Schrödinger equations, Part III. The nonlinear case. Journal of Computational and Applied Mathematics, 236(10), 182–204. https://doi.org/10.1016/j.cam.2014.06.012
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.
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Project title:
Adaptive Splitting for Nonlinear Schrödinger Equations: P24157-N13 (Fonds zur Förderung der wissenschaftlichen Forschung (FWF))
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Research Areas:
außerhalb der gesamtuniversitären Forschungsschwerpunkte: 100%