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Zeitschriftenartikel:

W. Auzinger, I. Brezinova, H. Hofstätter, O. Koch, M. Quell:
"Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part II: Comparison of local error estimation and step-selection strategies for nonlinear Schrödinger and wave equations";
angenommen für Computer Physics Communications.



Kurzfassung englisch:
We compare the practical performance of adaptive splitting methods for the solu-tion of nonlinear Schrödinger equations. Different methods for local error estima-tion are assessed with respect to their accuracy and efficiency in conjunction with promising strategies for step-size adaptation. The numerical comparisons com-prise the cubic nonlinear Schrödinger equation with a blow-up solution, systems of coupled nonlinear Schrödinger equations, a rotational and a Gross-Pitaevskii equation under a highly oscillatory potential inducing wave chaos, and a quantum control model with a time-dependent potential. Finally, for nonlinear wave equa-tions we demonstrate the enhanced computational stability ensuing from adaptive step selection strategies close to the border mandated by the CFL condition.

Schlagworte:
Nonlinear Schrödinger equations, splitting methods, local error estimators, adaptive step-size selection, embedded methods, defect-based


"Offizielle" elektronische Version der Publikation (entsprechend ihrem Digital Object Identifier - DOI)
http://dx.doi.org/10.1016/j.cpc.2018.08.003


Erstellt aus der Publikationsdatenbank der Technischen Universitšt Wien.