Adaptive splitting methods for nonlinear Schrodinger equations in the semiclassical regime

作者：Auzinger Winfried; Kassebacher Thomas^*; Koch Othmar; Thalhammer Mechthild

来源：Numerical Algorithms, 2016, 72(1): 1-35.

DOI：10.1007/s11075-015-0032-4

• Nonlinear Schrodinger equations
• Semiclassical regime
• Splitting methods
• Adaptive time integration
• Local error
• Convergence

The error behavior of exponential operator splitting methods for nonlinear Schrodinger 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.

• 出版日期2016-5