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W. Auzinger, T. Kassebacher, O. Koch, M. Thalhammer:
"Adaptive time-splitting methods for nonlinear Schrödinger equations in the semiclassical regime";
Vortrag: 11th Austrian Numerical Analysis Day, 2015, Linz; 06.05.2015 - 08.05.2015.

We consider nonlinear Schrödinger equations in the semiclassical
regime involving a small parameter a quadratic potential and
a cubic nonlinearity,
and study the error behavior of time-splitting methods, extending
earlier work. By suitable integral representations for the local
error of the Lie-Trotter and Strang splitting methods, we
deduce local error estimates that reflect the dependence on the time
step and the semiclassical parameter.
Numerical examples confirm these bounds. We also introduce a posteriori local error estimators
and illustrate their performance, in particular for adaptive
choice of the time steps.

Projektleitung Othmar Koch:
Adaptives Splitting für nichtlineare Schrödingergleichungen