Analysis of a splitting scheme for a class of nonlinear stochastic Schrödinger equations
Artikel i vetenskaplig tidskrift, 2023

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.

Geometric numerical integration

Stochastic partial differential equations

Strong convergence

Trace formulas

Stochastic Schrödinger equations

Splitting integrators

Författare

Charles-Edouard Bréhier

Université Claude-Bernard Lyon 1 (UCBL)

David Cohen

Umeå universitet

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Applied Numerical Mathematics

0168-9274 (ISSN)

Vol. 186 57-83

Numerisk analys och simulering av PDE med slumpmässig dispersion

Vetenskapsrådet (VR) (2018-04443), 2019-01-01 -- 2022-12-31.

Ämneskategorier

Beräkningsmatematik

Reglerteknik

Matematisk analys

DOI

10.1016/j.apnum.2023.01.002

Mer information

Senast uppdaterat

2023-01-30