Year: 2014
Communications in Computational Physics, Vol. 16 (2014), Iss. 1 : pp. 169–200
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.311012.191113a
Communications in Computational Physics, Vol. 16 (2014), Iss. 1 : pp. 169–200
Published online: 2014-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 32