Defect-based local error estimators for splitting methods, with application to Schrödinger equations, Part III. The nonlinear case

Abstract

The present work is concerned with the efficient time integration of nonlinear evolution equations by exponential operator splitting methods. Defect-based local error estimators serving as a reliable basis for adaptive stepsize control are constructed and analyzed. In the context of time-dependent nonlinear Schrödinger equations, asymptotical correctness of the local error estimators associated with the first-order Lie-Trotter and second-order Strang splitting methods is proven. Numerical examples confirm the theoretical results and illustrate the performance of adaptive stepsize control.