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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:273

Article

Auzinger, Winfried¹  Hofstaetter, Harald¹  Koch, Othmar¹  Thalhammer, Mechthild² 

[1] Vienna Univ Technol, Inst Anal & Sci Comp, A-1040 Vienna, Austria

[2] Leopold Franzens Univ Innsbruck, Inst Math, A-6020 Innsbruck, Austria

关键词: Nonlinear evolution equations;    Time-dependent nonlinear Schrodinger equations;    Exponential operator splitting methods;    A priori local error analysis;    A posteriori local error analysis;   

DOI  :  10.1016/j.cam.2014.06.012

来源: Elsevier

【 摘 要 】

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 Schrodinger 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. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

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