Asymptotic uniform estimate of random batch method with replacement for the Cucker-Smale model
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917048537317376 |
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| author | Jin, Shi Wang, Yuelin Wang, Yuliang |
| author_facet | Jin, Shi Wang, Yuelin Wang, Yuliang |
| contents | The Random Batch Method (RBM) [S. Jin, L. Li and J.-G. Liu, Random Batch Methods (RBM) for interacting particle systems, J. Comput. Phys. 400 (2020) 108877] is not only an efficient algorithm for simulating interacting particle systems, but also a randomly switching networked model for interacting particle system. This work investigates two RBM variants (RBM-r and RBM-1) applied to the Cucker-Smale flocking model. We establish the asymptotic emergence of global flocking and derive corresponding error estimates. By introducing a crucial auxiliary system and leveraging the intrinsic characteristics of the Cucker-Smale model, and under suitable conditions on the force, our estimates are uniform in both time and particle numbers. In the case of RBM-1, our estimates are sharper than those in Ha et al. (2021). Additionally, we provide numerical simulations to validate our analytical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15152 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotic uniform estimate of random batch method with replacement for the Cucker-Smale model Jin, Shi Wang, Yuelin Wang, Yuliang Numerical Analysis The Random Batch Method (RBM) [S. Jin, L. Li and J.-G. Liu, Random Batch Methods (RBM) for interacting particle systems, J. Comput. Phys. 400 (2020) 108877] is not only an efficient algorithm for simulating interacting particle systems, but also a randomly switching networked model for interacting particle system. This work investigates two RBM variants (RBM-r and RBM-1) applied to the Cucker-Smale flocking model. We establish the asymptotic emergence of global flocking and derive corresponding error estimates. By introducing a crucial auxiliary system and leveraging the intrinsic characteristics of the Cucker-Smale model, and under suitable conditions on the force, our estimates are uniform in both time and particle numbers. In the case of RBM-1, our estimates are sharper than those in Ha et al. (2021). Additionally, we provide numerical simulations to validate our analytical results. |
| title | Asymptotic uniform estimate of random batch method with replacement for the Cucker-Smale model |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2501.15152 |