Explicit pseudo-symplectic methods based on generating functions for stochastic Hamiltonian systems

摘要

We propose a systematic approach to construct explicit pseudo-symplectic schemes for stochastic Hamiltonian systems. This method is based on generating functions. so it is an extension of the techniques used for constructing high-order symplectic schemes for stochastic Hamiltonian systems. We study the order of convergence of the proposed explicit pseudo-symplectic schemes. The excellent long term performance of the pseudo-symplectic schemes is verified numerically. (C) 2019 Elsevier B.V. All rights reserved.