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High-Order Symplectic Schemes for Stochastic Hamiltonian Systems

Published online by Cambridge University Press:  03 June 2015

Jian Deng ,
Cristina Anton  and
Yau Shu Wong
Jian Deng*
Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2G1, Canada
Cristina Anton*
Affiliation:
Department of Mathematics and Statistics, Grant MacEwan University, Edmonton, AB T5J 4S2, Canada
Yau Shu Wong*
Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2G1, Canada
*
Corresponding author.Email:deng2@ualberta.ca
Email:popescuc@macewan.ca
Email:yaushu.wong@ualberta.ca
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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.

Keywords

60H1065C3065P10Stochastic Hamiltonian systemssymplectic integrationmean-square convergencehigh-order schemes.
Type
Research Article
Information
Communications in Computational Physics , Volume 16 , Issue 1 , July 2014 , pp. 169 - 200
Copyright
Copyright © Global Science Press Limited 2014

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