Article ID Journal Published Year Pages File Type
4638836 Journal of Computational and Applied Mathematics 2015 23 Pages PDF
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.

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Physical Sciences and Engineering Mathematics Applied Mathematics
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