On Fourier time-splitting methods for nonlinear Schrodinger equations in the semi-classical limit II. Analytic regularity
Résumé
We consider the time discretization based on Lie-Trotter splitting, for the
nonlinear Schrodinger equation, in the semi-classical limit, with
initial data under the form of WKB states. We show that both the
exact and the numerical solutions keep a WKB structure, on a time
interval independent of the Planck constant. We prove error
estimates, which show that the quadratic observables can be computed
with a time step independent of the Planck constant. The functional
framework is based on time-dependent analytic spaces, in order to
overcome a previously encountered loss of regularity phenomenon.
Origine : Fichiers produits par l'(les) auteur(s)
Loading...