Volume 11, Issue 3
Symplectic Schemes for Stochastic Hamiltonian Systems Preserving Hamiltonian Functions

C. Anton, Y. Wong & J. Deng

DOI:

Int. J. Numer. Anal. Mod., 11 (2014), pp. 427-451

Published online: 2014-11

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  • Abstract

We present high-order symplectic schemes for stochastic Hamiltonian systems pre-serving Hamiltonian functions. The approach is based on the generating function method, and we prove that the coefficients of the generating function are invariant under permutations for this class of systems. As a consequence, the proposed high-order symplectic weak and strong schemes are computationally efficient because they require less stochastic multiple integrals than the Taylor expansion schemes with the same order.

  • Keywords

Stochastic Hamiltonian systems generating function symplectic method high-order schemes

  • AMS Subject Headings

65C30 60H35 37J10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-11-427, author = {C. Anton, Y. Wong and J. Deng}, title = {Symplectic Schemes for Stochastic Hamiltonian Systems Preserving Hamiltonian Functions}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2014}, volume = {11}, number = {3}, pages = {427--451}, abstract = {We present high-order symplectic schemes for stochastic Hamiltonian systems pre-serving Hamiltonian functions. The approach is based on the generating function method, and we prove that the coefficients of the generating function are invariant under permutations for this class of systems. As a consequence, the proposed high-order symplectic weak and strong schemes are computationally efficient because they require less stochastic multiple integrals than the Taylor expansion schemes with the same order.}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/536.html} }
TY - JOUR T1 - Symplectic Schemes for Stochastic Hamiltonian Systems Preserving Hamiltonian Functions AU - C. Anton, Y. Wong & J. Deng JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 427 EP - 451 PY - 2014 DA - 2014/11 SN - 11 DO - http://dor.org/ UR - https://global-sci.org/intro/article_detail/ijnam/536.html KW - Stochastic Hamiltonian systems KW - generating function KW - symplectic method KW - high-order schemes AB - We present high-order symplectic schemes for stochastic Hamiltonian systems pre-serving Hamiltonian functions. The approach is based on the generating function method, and we prove that the coefficients of the generating function are invariant under permutations for this class of systems. As a consequence, the proposed high-order symplectic weak and strong schemes are computationally efficient because they require less stochastic multiple integrals than the Taylor expansion schemes with the same order.
C. Anton, Y. Wong & J. Deng. (1970). Symplectic Schemes for Stochastic Hamiltonian Systems Preserving Hamiltonian Functions. International Journal of Numerical Analysis and Modeling. 11 (3). 427-451. doi:
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