W. Auzinger, H. Hofstätter, O. Koch, K. Kropielnicka, P. Singh:
"Time adaptive Zassenhaus splittings for the Schrödinger equation in the semiclassical regime";
Applied Mathematics and Computation, 362 [124550] (2019).

Kurzfassung englisch:
Time dependent Schrödinger equations with conservative force field commonly
constitute a major challenge in the numerical approximation, especially
when they are analysed in the semiclassical regime. Extremely high
oscillations originate from the semiclassical parameter, and call for
appropriate methods. We propose to employ a combination of asymptotic
Zassenhaus splitting with time adaptivity. While the former turns the
disadvantage of the semiclassical parameter into an advantage, leading to
highly efficient methods with low error constants, the latter enables to
choose an optimal time step and to speed up the calculations when the
oscillations subside. We support the results with numerical examples.

Numerical time integration, time adaptivity, splitting schemes, asymptotic splittings

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