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arXiv · 2410.22359

Low regularity symplectic schemes for stochastic NLS

Jacob Armstrong-Goodall·Yvain Bruned
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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.

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Jacob Armstrong-Goodall, Yvain Bruned. 2024-10-21. Low regularity symplectic schemes for stochastic NLS. https://arxiv.org/abs/2410.22359

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