Low regularity symplectic schemes for stochastic NLS
Analysis of PDEs
2026-04-08 v2 Numerical Analysis
Numerical Analysis
Probability
Abstract
We introduce a class of symplectic resonance based schemes for Schr\"odinger's equation in dimension one, building on the work in [1] wherein resonance based numerical schemes were developed in the context of dispersive PDE driven by time dependent, or space-time dependent, coloured noise. We work primarily with a cubic nonlinearity, advancing the approach introduced in [15] for deriving symplectic schemes in the deterministic setting. As an example of such a scheme we derive the resonance based midpoint rule for the Stochastic NLS and analyse its convergence properties.
Cite
@article{arxiv.2410.22359,
title = {Low regularity symplectic schemes for stochastic NLS},
author = {Jacob Armstrong-Goodall and Yvain Bruned},
journal= {arXiv preprint arXiv:2410.22359},
year = {2026}
}
Comments
40 pages, 8 figures