Splitting Methods For Solving A Class Of Stochastic Hamiltonian Systems

Considering the symmetric splitting methods to approximate 2n-dimensional stochastic Hamiltonian systems by decomposing these vector fields into two n-dimensional vector fields and treat them separately.Then the numerical solutions approximating the exact flows of two vector fields are calculated by the midpoint scheme respectively.And the exact flow of the2n-dimensional Hamiltonian system is approximated by the symmetric composition method corresponding to the symmetric splitting methods,which is realized by three stages.By using Milstein’s scheme and Taylor Expansion,the convergence order of the iterative scheme generated by splitting methods is obtained,which is of the same order as the Milstein’s scheme.Two numerical experiments are presented to verify the theoretical analysis and show the advantage of this method.