论文标题
随机泊松系统的结构保存数值方法
Structure-preserving numerical methods for stochastic Poisson systems
论文作者
论文摘要
我们为随机泊松系统（SPSS）提出了一类数值集成方法。基于Darboux-lie定理，我们通过通过求解由SPSS的Poisson支架定义的某些PDE的典型坐标转换来将SPSS转换为其规范形式，即广义的Hamiltonian Systems（SHSS）。然后，使用[0,1]中的α\生成a-eneration函数方法来创建SHSS的符合性离散化，然后通过逆坐标转换向SPSS的数值积分器进行了转换。事实证明，这些集成剂可以保留SPSS的泊松结构和Casimir功能。应用于三维随机刚性身体系统和三维随机Lotka-Volterra系统的应用显示了所提出的方法的效率。
We propose a class of numerical integration methods for stochastic Poisson systems (SPSs) of arbitrary dimensions. Based on the Darboux-Lie theorem, we transform the SPSs to their canonical form, the generalized stochastic Hamiltonian systems (SHSs), via canonical coordinate transformations found by solving certain PDEs defined by the Poisson brackets of the SPSs. An a-generating function approach with α\in [0,1] is then used to create symplectic discretizations of the SHSs, which are then transformed back by the inverse coordinate transformation to numerical integrators for the SPSs. These integrators are proved to preserve both the Poisson structure and the Casimir functions of the SPSs. Applications to a three-dimensional stochastic rigid body system and a three-dimensional stochastic Lotka-Volterra system show efficiency of the proposed methods.
