Weak and Strong Order of Convergence of a Semidiscrete Scheme for the Stochastic Nonlinear Schrodinger Equation

Anne de Bouard (1) , Arnaud Debussche (2)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 IRMAR - Institut de Recherche Mathématique de Rennes

In this article we analyze the error of a semidiscrete scheme for the stochastic nonlinear Schrodinger equation with power nonlinearity. We consider supercritical or subcritical nonlinearity and the equation can be either focusing or defocusing. Allowing sufficient spatial regularity we prove that the numerical scheme has strong order in general and order 1 if the noise is additive. Furthermore, we also prove that the weak order is always 1

Domaines: Statistiques [math.ST]; Analyse numérique [math.NA]

Anne de Bouard, Arnaud Debussche. Weak and Strong Order of Convergence of a Semidiscrete Scheme for the Stochastic Nonlinear Schrodinger Equation. Applied Mathematics and Optimization, 2006, 54 (3), pp.369-399. ⟨10.1007/s00245-006-0875-0⟩. ⟨hal-00383314⟩