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Volume 19, Issue 2-3
Structure-Preserving Numerical Methods for a Class of Stochastic Poisson Systems

Yuchao Wang, Lijin Wang & Yanzhao Cao

Int. J. Numer. Anal. Mod., 19 (2022), pp. 194-219.

Published online: 2022-04

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  • Abstract

We propose a type of numerical methods for a class of stochastic Poisson systems with invariant energy. The proposed numerical methods preserve both the energy and the Casimir functions of the systems. In addition, we provide a new approach of constructing stochastic Poisson integrators which respect the Poisson structure and the Casimir functions of stochastic Poisson systems based on coordinate transformations on the midpoint method. Numerical tests are performed to demonstrate our theoretical analysis.

  • Keywords

stochastic Poisson systems, structure-preserving algorithms, Poisson structure, Casimir functions, Poisson integrators.

  • AMS Subject Headings

60H35, 60H15, 65C30, 60H10, 65D30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-19-194, author = {Wang , YuchaoWang , Lijin and Cao , Yanzhao}, title = {Structure-Preserving Numerical Methods for a Class of Stochastic Poisson Systems}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2022}, volume = {19}, number = {2-3}, pages = {194--219}, abstract = {

We propose a type of numerical methods for a class of stochastic Poisson systems with invariant energy. The proposed numerical methods preserve both the energy and the Casimir functions of the systems. In addition, we provide a new approach of constructing stochastic Poisson integrators which respect the Poisson structure and the Casimir functions of stochastic Poisson systems based on coordinate transformations on the midpoint method. Numerical tests are performed to demonstrate our theoretical analysis.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/20477.html} }
TY - JOUR T1 - Structure-Preserving Numerical Methods for a Class of Stochastic Poisson Systems AU - Wang , Yuchao AU - Wang , Lijin AU - Cao , Yanzhao JO - International Journal of Numerical Analysis and Modeling VL - 2-3 SP - 194 EP - 219 PY - 2022 DA - 2022/04 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/20477.html KW - stochastic Poisson systems, structure-preserving algorithms, Poisson structure, Casimir functions, Poisson integrators. AB -

We propose a type of numerical methods for a class of stochastic Poisson systems with invariant energy. The proposed numerical methods preserve both the energy and the Casimir functions of the systems. In addition, we provide a new approach of constructing stochastic Poisson integrators which respect the Poisson structure and the Casimir functions of stochastic Poisson systems based on coordinate transformations on the midpoint method. Numerical tests are performed to demonstrate our theoretical analysis.

Wang , YuchaoWang , Lijin and Cao , Yanzhao. (2022). Structure-Preserving Numerical Methods for a Class of Stochastic Poisson Systems. International Journal of Numerical Analysis and Modeling. 19 (2-3). 194-219. doi:
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