Analysis of a splitting scheme for a class of nonlinear stochastic Schrödinger equations

07/05/2020
by   Charles-Edouard Bréhier, et al.
0

We analyze the qualitative properties and the order of convergence of a splitting scheme for a class of nonlinear stochastic Schrödinger equations driven by additive Itô noise. The class of nonlinearities of interest includes nonlocal interaction cubic nonlinearities. We show that the numerical solution is symplectic and preserves the expected mass for all times. On top of that, for the convergence analysis, some exponential moment bounds for the exact and numerical solutions are proved. This enables us to provide strong orders of convergence as well as orders of convergence in probability and almost surely. Finally, extensive numerical experiments illustrate the performance of the proposed numerical scheme.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

09/24/2019

Strang splitting schemes for N-level Bloch models

We extend to the N-level Bloch model the splitting scheme which use exac...
07/20/2019

Drift-preserving numerical integrators for stochastic Hamiltonian systems

The paper deals with numerical discretizations of separable nonlinear Ha...
05/11/2020

Exponential integrators for the stochastic Manakov equation

This article presents and analyses an exponential integrator for the sto...
12/17/2021

An adaptive splitting method for the Cox-Ingersoll-Ross process

We propose a new splitting method for strong numerical solution of the C...
10/28/2020

Lie-Trotter Splitting for the Nonlinear Stochastic Manakov System

This article analyses the convergence of the Lie-Trotter splitting schem...
05/26/2020

Drift-preserving numerical integrators for stochastic Poisson systems

We perform a numerical analysis of randomly perturbed Poisson systems. F...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.