Strong Rates of Convergence of a Splitting Scheme for Schrödinger Equations with Nonlocal Interaction Cubic Nonlinearity and White Noise Dispersion
Journal article, 2022

We analyze a splitting integrator for the time discretization of the Schrodinger equation with nonlocal interaction cubic nonlinearity and white noise dispersion. We prove that this time integrator has order of convergence one in the pth mean sense, for any p > 1 in some Sobolev spaces. We prove that the splitting schemes preserves the L2-norm, which is a crucial property for the proof of the strong convergence result. Finally, numerical experiments illustrate the performance of the proposed numerical scheme.

strong convergence rates

stochastic Schródinger equations

splitting integrators

white noise dispersion

nonlocal interaction cubic nonlinearity

Author

Charles-Edouard Bréhier

Université de Lyon

David Cohen

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

SIAM-ASA Journal on Uncertainty Quantification

21662525 (eISSN)

Vol. 10 1 453-480

Numerical analysis and simulation of PDEs with random dispersion

Swedish Research Council (VR) (2018-04443), 2019-01-01 -- 2022-12-31.

Subject Categories

Computational Mathematics

Control Engineering

Mathematical Analysis

DOI

10.1137/20M1378168

More information

Latest update

7/4/2022 1