Symplectic Integrators to Stochastic Hamiltonian Dynamical Systems Derived from Composition Methods
نویسنده
چکیده
“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.
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