On Fourier time-splitting methods for nonlinear Schrodinger equations in   the semi-classical limit II. Analytic regularity
  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. 
R\'emi Carles (IMAG), Cl\'ement Gallo (IMAG)
math.NA math.AP