Structure-Preserving Implicit Runge-Kutta Methods for Stochastic Poisson Systems with Multiple Noises
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915115815665664 |
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| author | Zhang, Liying Xue, Fenglin Wang, Lijin |
| author_facet | Zhang, Liying Xue, Fenglin Wang, Lijin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12778 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Structure-Preserving Implicit Runge-Kutta Methods for Stochastic Poisson Systems with Multiple Noises Zhang, Liying Xue, Fenglin Wang, Lijin Numerical Analysis 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. |
| title | Structure-Preserving Implicit Runge-Kutta Methods for Stochastic Poisson Systems with Multiple Noises |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2501.12778 |