Uniformly accurate exponential-type integrators for Klein-Gordon equations with asymptotic convergence to classical splitting schemes in the nonlinear Schrödinger limit - Université de Rennes Accéder directement au contenu
Article Dans Une Revue Mathematics of Computation Année : 2018

Uniformly accurate exponential-type integrators for Klein-Gordon equations with asymptotic convergence to classical splitting schemes in the nonlinear Schrödinger limit

Résumé

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 non-relativistic regime without any step-size restriction, and under the same regularity assumptions on the initial data required for the integration of the corresponding limit system. In contrast to previous works we do not employ any asymptotic/multiscale expansion of the solution. This allows us derive uniform convergent schemes under far weaker regularity assumptions on the exact solution. In particular, the newly derived exponential-type integrators of first-, respectively, second-order converge in the non-relativistic limit to the classical Lie, respectively, Strang splitting in the nonlinear Schrödinger limit.
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Dates et versions

hal-01331949 , version 1 (14-06-2016)
hal-01331949 , version 2 (16-01-2017)

Identifiants

Citer

Simon Baumstark, Erwan Faou, Katharina Schratz. Uniformly accurate exponential-type integrators for Klein-Gordon equations with asymptotic convergence to classical splitting schemes in the nonlinear Schrödinger limit. Mathematics of Computation, 2018, 87 (311), pp.1227-1254. ⟨10.1090/mcom/3263⟩. ⟨hal-01331949v2⟩
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