2025/01/22 by Liying Zhang, Zhang, Liying, Fenglin Xue +3
Decision Sciences · Physics and Astronomy · #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design #Simulation Techniques and Applications
paper · pdf · doi:10.48550/arxiv.2501.12778
openalex publication_date 2025/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we propose the diagonal implicit Runge-Kutta methods and transformed Runge-Kutta methods for stochastic Poisson systems with multiple noises. We prove that the first methods can preserve the Poisson structure, Casimir functions, and quadratic Hamiltonian functions in the case of constant structure matrix. Darboux-Lie theorem combined with coordinate transformation is used to construct the transformed Runge-Kutta methods for the case of non-constant structure matrix that preserve both the Poisson structure and the Casimir functions. Finally, through numerical experiments on stochastic rigid body systems and linear stochastic Poisson systems, the structure-preserving properties of the proposed two kinds of numerical methods are effectively verified.