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Volume 4, Issue 1
On Global Error of Symplectic Schemes for Stochastic Hamiltonian Systems

CRISTINA A. ANTON, YAUSHU WONG, AND JIAN DENG

Int. J. Numer. Anal. Mod. B, 4 (2013), pp. 80-93

Published online: 2013-04

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  • Abstract
We investigate a first order weak symplectic numerical scheme for stochastic Hamiltonian systems. Given the solution (X_t) and a class of functions f, we derive the expansion of the global approximation error for the computed E(f(X_t)) in powers of the discretization step size. The present study is an extension of the results obtained by Talay and Tubaro for the explicit Euler scheme. Based on the derived global error expansion, we construct an extrapolation method of the weak second order. The performance of the extrapolation method is demonstrated numerically for a model simulating oscillations of the particles in storage rings.
  • Keywords

Stochastic Hamiltonian system symplectic methods numerical weak schemes extrapolation method

  • AMS Subject Headings

65C30 60H35 37J10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAMB-4-80, author = {CRISTINA A. ANTON, YAUSHU WONG, AND JIAN DENG}, title = {On Global Error of Symplectic Schemes for Stochastic Hamiltonian Systems}, journal = {International Journal of Numerical Analysis Modeling Series B}, year = {2013}, volume = {4}, number = {1}, pages = {80--93}, abstract = {We investigate a first order weak symplectic numerical scheme for stochastic Hamiltonian systems. Given the solution (X_t) and a class of functions f, we derive the expansion of the global approximation error for the computed E(f(X_t)) in powers of the discretization step size. The present study is an extension of the results obtained by Talay and Tubaro for the explicit Euler scheme. Based on the derived global error expansion, we construct an extrapolation method of the weak second order. The performance of the extrapolation method is demonstrated numerically for a model simulating oscillations of the particles in storage rings.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnamb/247.html} }
TY - JOUR T1 - On Global Error of Symplectic Schemes for Stochastic Hamiltonian Systems AU - CRISTINA A. ANTON, YAUSHU WONG, AND JIAN DENG JO - International Journal of Numerical Analysis Modeling Series B VL - 1 SP - 80 EP - 93 PY - 2013 DA - 2013/04 SN - 4 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnamb/247.html KW - Stochastic Hamiltonian system KW - symplectic methods KW - numerical weak schemes KW - extrapolation method AB - We investigate a first order weak symplectic numerical scheme for stochastic Hamiltonian systems. Given the solution (X_t) and a class of functions f, we derive the expansion of the global approximation error for the computed E(f(X_t)) in powers of the discretization step size. The present study is an extension of the results obtained by Talay and Tubaro for the explicit Euler scheme. Based on the derived global error expansion, we construct an extrapolation method of the weak second order. The performance of the extrapolation method is demonstrated numerically for a model simulating oscillations of the particles in storage rings.
CRISTINA A. ANTON, YAUSHU WONG, AND JIAN DENG. (2013). On Global Error of Symplectic Schemes for Stochastic Hamiltonian Systems. International Journal of Numerical Analysis Modeling Series B. 4 (1). 80-93. doi:
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