On time splitting methods for nonlinear Schrodinger equations in the semi-classical limit

Rémi Carles (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

We prove a global error estimate for a Lie-Trotter splitting operator associated to the Schrodinger-Poisson equation in the semiclassical regime, when the WKB approximation is valid. So long as the solution to a compressible Euler-Poisson equation is smooth, the error between the numerical solution and the exact solution is controlled in Sobolev spaces, in a suitable phase/amplitude representation. As a corollary, we infer the numerical convergence of the quadratic observables with a time step independent of the Planck constant. A similar result is established for the nonlinear Schrodinger equation in the weakly nonlinear regime.

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Rémi Carles. On time splitting methods for nonlinear Schrodinger equations in the semi-classical limit. 2012. ⟨hal-00733128v1⟩