Iterative Splitting Method as Almost Asymptotic Symplectic Integrator for Stochastic Nonlinear Schrodinger Equation

摘要

In this paper, we present splitting methods which are based on iterative schemes and applied to stochastic nonlinear Schrodinger 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 deterministic and stochastic parts, 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 Schrodunger equation are presented.