Uniformly accurate exponential-type integrators for Klein-Gordon equations with asymptotic convergence to the classical NLS splitting

Simon Baumstark, Erwan Faou, Katharina Schratz

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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.
Original languageEnglish
Pages (from-to)1227-1254
Number of pages28
JournalMathematics of Computation
Volume87
Issue number311
Early online date15 Aug 2017
DOIs
Publication statusPublished - May 2018

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