Iterative Splitting Methods: Almost Asymptotic Symplectic Integrator for Stochastic Nonlinear Schrödinger Equation
For researchers in stochastic PDEs and numerical analysis, this provides an almost symplectic integrator for a specific equation, but the approach is incremental as it builds on existing iterative splitting and symplectic integration techniques.
The paper develops iterative splitting methods for the stochastic nonlinear Schrödinger equation that almost conserve symplectic structure, achieving accelerated computation by decoupling deterministic and stochastic parts solved analytically.
In this paper we present splitting methods which are based on iterative schemes and applied to stochastic nonlinear Schroedinger equation. We will design stochastic integrators which almost conserve the symplectic structure. The idea is based on rewriting an iterative splitting approach as a successive approximation method based on a contraction mapping principle and that we have an almost symplectic scheme. We apply a stochastic differential equation, that we can decouple into a deterministic and stochatic part, while each part can be solved analytically. Such decompositions allow accelerating the methods and preserving, under suitable conditions, the symplecticity of the schemes. A numerical analysis and application to the stochastic Schroedinger equation are presented.