Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 384937, 12 pages
Research Article

Symplectic Integrators to Stochastic Hamiltonian Dynamical Systems Derived from Composition Methods

Faculty of Economics, Nagoya City University, Nagoya 467-8501, Japan

Received 25 December 2009; Accepted 20 June 2010

Academic Editor: Katica R. (Stevanovic) Hedrih

Copyright © 2010 Tetsuya Misawa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


“Symplectic” schemes for stochastic Hamiltonian dynamical systems are formulated through “composition methods (or operator splitting methods)” proposed by Misawa (2001). In the proposed methods, a symplectic map, which is given by the solution of a stochastic Hamiltonian system, is approximated by composition of the stochastic flows derived from simpler Hamiltonian vector fields. The global error orders of the numerical schemes derived from the stochastic composition methods are provided. To examine the superiority of the new schemes, some illustrative numerical simulations on the basis of the proposed schemes are carried out for a stochastic harmonic oscillator system.