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arXiv · 2501.15152

Asymptotic uniform estimate of random batch method with replacement for the Cucker-Smale model

Shi Jin·Yuelin Wang·Yuliang Wang
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Abstract

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.

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Shi Jin, Yuelin Wang, Yuliang Wang. 2025-01-25. Asymptotic uniform estimate of random batch method with replacement for the Cucker-Smale model. https://arxiv.org/abs/2501.15152

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