High-Order Symplectic Schemes for Stochastic Hamiltonian Systems  

作　　者：Jian Deng Cristina Anton Yau Shu Wong 

机构地区：[1]Department of Mathematical and Statistical Sciences,University of Alberta,Edmonton,AB T6G 2G1,Canada. [2]Department of Mathematics and Statistics,Grant MacEwan University,Edmonton,AB T5J 4S2,Canada.

出　　处：《Communications in Computational Physics》2014年第6期169-200,共32页计算物理通讯（英文）

摘　　要：The construction of symplectic numerical schemes for stochastic Hamiltonian systems is studied.An approach based on generating functions method is proposed to generate the stochastic symplectic integration of any desired order.In general the proposed symplectic schemes are fully implicit,and they become computationally expensive for mean square orders greater than two.However,for stochastic Hamiltonian systems preserving Hamiltonian functions,the high-order symplectic methods have simpler forms than the explicit Taylor expansion schemes.A theoretical analysis of the convergence and numerical simulations are reported for several symplectic integrators.The numerical case studies confirm that the symplectic methods are efficient computational tools for long-term simulations.

关 键 词：Stochastic Hamiltonian systems symplectic integration mean-square convergence high-order schemes. 

分 类 号：O17[理学—数学]