Adaptive splitting methods for nonlinear Schrödinger equations in the semiclassical regime
For researchers solving nonlinear Schrödinger equations in the semiclassical regime, this work provides a theoretical foundation and practical error estimators for adaptive time-stepping, though it is an incremental contribution to existing splitting methods.
The paper analyzes the error behavior of Lie and Strang splitting methods for nonlinear Schrödinger equations in the semiclassical regime, identifying the dependence on the semiclassical parameter and proposing a posteriori local error estimators for adaptive time-stepping. Numerical examples validate the theoretical results.
The error behavior of exponential operator splitting methods for nonlinear Schr{ö}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.