Buchbeiträge:
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";
in: "ASC Report 14/2017",
herausgegeben von: Institute for Analysis and Scientific Computing;
Vienna University of Technology,
Wien,
2017,
ISBN: 978-3-902627-10-0,
S. 1
- 40.
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
Elektronische Version der Publikation:
http://www.asc.tuwien.ac.at/preprint/2017/asc14x2017.pdf
Erstellt aus der Publikationsdatenbank der Technischen Universität Wien.