Communications in Mathematical Sciences
- Commun. Math. Sci.
- Volume 4, Number 4 (2006), 679-705.
On a splitting scheme for the nonlinear Schrödinger equation in a random medium
In this paper we consider a nonlinear Schrödinger equation (NLS) with random coefficients, in a regime of separation of scales corresponding to diffusion approximation. The primary goal of this paper is to propose and study an efficient numerical scheme in this framework. We use a pseudo-spectral splitting scheme and we establish the order of the global error. In particular we show that we can take an integration step larger than the smallest scale of the problem, here the correlation length of the random medium. We study the asymptotic behavior of the numerical solution in the diffusion approximation regime.
Commun. Math. Sci., Volume 4, Number 4 (2006), 679-705.
First available in Project Euclid: 5 April 2007
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15] 60F05: Central limit and other weak theorems 65M70: Spectral, collocation and related methods
Marty, Renaud. On a splitting scheme for the nonlinear Schrödinger equation in a random medium. Commun. Math. Sci. 4 (2006), no. 4, 679--705. https://projecteuclid.org/euclid.cms/1175797606