Communications in Mathematical Sciences

Volume 19 (2021)

Number 4

Local error of a splitting scheme for a nonlinear Schrödinger-type equation with random dispersion

Pages: 1051 – 1069

DOI: https://dx.doi.org/10.4310/CMS.2021.v19.n4.a8

Author

Renaud Marty (Institut Élie Cartan de Lorraine, Université de Lorraine, Vandoeuvre-lès-Nancy, France)

Abstract

We study a Lie splitting scheme for a nonlinear Schrödinger-type equation with random dispersion. The main result is an approximation of the local error. Then we can deduce sharp order estimates, for instance in the case of a white noise dispersion.

Keywords

splitting schemes, nonlinear Schrödinger-type equations, stochastic partial differential equations

2010 Mathematics Subject Classification

35Q55, 60H15, 60H35, 65M15

Received 21 October 2019

Accepted 4 December 2020

Published 18 June 2021