Uniformly accurate exponential-type integrators for Klein-Gordon equations with asymptotic convergence to the classical NLS splitting
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- by Simon Baumstark, Erwan Faou and Katharina Schratz PDF
- Math. Comp. 87 (2018), 1227-1254 Request permission
Abstract:
We introduce efficient and robust exponential-type integrators for Klein-Gordon equations which resolve the solution in the relativistic regime as well as in the highly-oscillatory nonrelativistic regime without any step-size restriction under the same regularity assumptions on the initial data required for the integration of the corresponding nonlinear Schrödinger limit system. In contrast to previous works we do not employ any asymptotic/multiscale expansion of the solution. This allows us to derive uniform convergent schemes under far weaker regularity assumptions on the exact solution. In addition, the newly derived first- and second-order exponential-type integrators converge to the classical Lie, respectively, Strang splitting in the nonlinear Schrödinger limit.References
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Additional Information
- Simon Baumstark
- Affiliation: Fakultät für Mathematik, Karlsruhe Institute of Technology, Englerstrasse 2, 76131 Karlsruhe, Germany
- Email: simon.baumstark@kit.edu
- Erwan Faou
- Affiliation: INRIA & ENS Rennes, Avenue Robert Schumann F-35170 Bruz, France
- MR Author ID: 656335
- Email: Erwan.Faou@inria.fr
- Katharina Schratz
- Affiliation: Fakultät für Mathematik, Karlsruhe Institute of Technology, Englerstrasse 2, 76131 Karlsruhe, Germany
- MR Author ID: 990639
- Email: katharina.schratz@kit.edu
- Received by editor(s): June 17, 2016
- Received by editor(s) in revised form: November 1, 2016
- Published electronically: August 15, 2017
- Additional Notes: The authors gratefully acknowledge financial support by the Deutsche Forschungsgemeinschaft (DFG) through CRC 1173. This work was also partly supported by the ERC Starting Grant Project GEOPARDI No 279389.
- © Copyright 2017 American Mathematical Society
- Journal: Math. Comp. 87 (2018), 1227-1254
- MSC (2010): Primary 35C20, 65M12, 35L05
- DOI: https://doi.org/10.1090/mcom/3263
- MathSciNet review: 3766386