article

Radoin Belaouar and Anne de Bouard and Arnaud Debussche


Modelisation Group (2015) : Numerical analysis of the nonlinear Schrödinger equation with white noise dispersion




Numerical analysis of the nonlinear Schrödinger equation with white noise dispersion

Radoin Belaouar and Anne de Bouard and Arnaud Debussche




article

Stochastic Partial Differential Equations: Analysis and Computations

Springer US

This article is devoted to the numerical study of a nonlinear Schrödinger equation in which the coefficient in front of the group velocity dispersion is multiplied by a real valued Gaussian white noise. We first perform the numerical analysis of a semi-discrete Crank-Nicolson scheme in the case when the continuous equation possesses a unique global solution. We prove that the strong order of convergence in probability is equal to one in this case. In a second step, we numerically investigate, in space dimension one, the behavior of the solutions of the equation for different power nonlinearities, corresponding to subcritical, critical or supercritical nonlinearities in the deterministic case. Numerical evidence of a change in the critical power due to the presence of the noise is pointed out.

To cite this publication :


Radoin Belaouar, Anne de Bouard, Arnaud Debussche: Numerical analysis of the nonlinear Schrödinger equation with white noise dispersion. Dans: Stochastic Partial Differential Equations: Analysis and Computations, 3 (1), p. 103-132, 2015, ISSN: 2194-0401.





Candidature
Documentation

En savoir plus ?

Contactez-nous et téléchargez une documentation


Aussi intéressé(e) par :