Adaptive splitting methods for nonlinear Schr\"{o}dinger equations in the semiclassical regime
Numerical Analysis
2016-05-03 v1
Abstract
The error behavior of exponential operator splitting methods for nonlinear Schr{\"o}dinger equations in the semiclassical regime is studied. For the Lie and Strang splitting methods, the exact form of the local error is determined and the dependence on the semiclassical parameter is identified. This is enabled within a defect-based framework which also suggests asymptotically correct a~posteriori local error estimators as the basis for adaptive time stepsize selection. Numerical examples substantiate and complement the theoretical investigations.
Cite
@article{arxiv.1605.00429,
title = {Adaptive splitting methods for nonlinear Schr\"{o}dinger equations in the semiclassical regime},
author = {Winfried Auzinger and Thomas Kassebacher and Othmar Koch and Mechthild Thalhammer},
journal= {arXiv preprint arXiv:1605.00429},
year = {2016}
}