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W. Auzinger, T. Kassebacher, O. Koch, M. Thalhammer:
"Adaptive splitting methods for nonlinear Schrödinger equations in the semiclassical regime";
Numerical Algorithms, 72 (2016), 1; 1 - 35.

The convergence of exponential splitting methods for nonlinear Schrödinger 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 error estimators as the basis for adaptive time stepping. Numerical examples, also including higher-order schemes, confirm the theoretical results.

Nonlinear Schrödinger equations, semiclassical regime, splitting methods,

http://dx.doi.org/10.1007/s11075-015-0032-4

http://link.springer.com/article/10.1007/s11075-015-0032-4

Project Head Othmar Koch:
Adaptives Splitting für nichtlineare Schrödingergleichungen