2014/12/03 by Jürgen Geiser, Geiser, Juergen
Mathematics · Economics, Econometrics and Finance · Earth and Planetary Sciences · #Numerical methods for differential equations #Stochastic processes and financial applications #Meteorological Phenomena and Simulations
paper · pdf · doi:10.48550/arxiv.1412.1363
In this paper we present splitting methods which are based on iterative\nschemes and applied to stochastic nonlinear Schroedinger equation. We will\ndesign stochastic integrators which almost conserve the symplectic structure.\nThe idea is based on rewriting an iterative splitting approach as a successive\napproximation method based on a contraction mapping principle and that we have\nan almost symplectic scheme. We apply a stochastic differential equation, that\nwe can decouple into a deterministic and stochatic part, while each part can be\nsolved analytically. Such decompositions allow accelerating the methods and\npreserving, under suitable conditions, the symplecticity of the schemes. A\nnumerical analysis and application to the stochastic Schroedinger equation are\npresented.\n