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Volume 16, Issue 1
High-Order Symplectic Schemes for Stochastic Hamiltonian Systems

Jian Deng, Cristina Anton & Yau Shu Wong

Commun. Comput. Phys., 16 (2014), pp. 169-200.

Published online: 2014-07

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  • 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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@Article{CiCP-16-169, author = {}, title = {High-Order Symplectic Schemes for Stochastic Hamiltonian Systems}, journal = {Communications in Computational Physics}, year = {2014}, volume = {16}, number = {1}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.311012.191113a}, url = {http://global-sci.org/intro/article_detail/cicp/7038.html} }
TY - JOUR T1 - High-Order Symplectic Schemes for Stochastic Hamiltonian Systems JO - Communications in Computational Physics VL - 1 SP - 169 EP - 200 PY - 2014 DA - 2014/07 SN - 16 DO - http://doi.org/10.4208/cicp.311012.191113a UR - https://global-sci.org/intro/article_detail/cicp/7038.html KW - AB -

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.

Jian Deng, Cristina Anton & Yau Shu Wong. (2020). High-Order Symplectic Schemes for Stochastic Hamiltonian Systems. Communications in Computational Physics. 16 (1). 169-200. doi:10.4208/cicp.311012.191113a
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