Low regularity symplectic schemes for stochastic NLS
This work provides incremental improvements to numerical methods for stochastic dispersive PDEs, targeting researchers in computational mathematics and physics.
The authors developed symplectic resonance-based numerical schemes for solving the one-dimensional stochastic nonlinear Schrödinger equation with cubic nonlinearity, building on prior deterministic and stochastic methods, and analyzed the convergence properties of their proposed resonance-based midpoint rule.
We introduce a class of symplectic resonance based schemes for Schrödinger'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.