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.