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

• Autores: Winfried Auzinger, Harald Hofstätter, Othmar Koch, Mechthild Thalhammer
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 273, Nº 1, 2015, págs. 182-204
• Idioma: inglés
• DOI: 10.1016/j.cam.2014.06.012
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• Resumen

  • 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.