Asymptotic uniform estimate of random batch method with replacement for the Cucker-Smale model
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.
Cite
@article{arxiv.2501.15152,
title = {Asymptotic uniform estimate of random batch method with replacement for the Cucker-Smale model},
author = {Shi Jin and Yuelin Wang and Yuliang Wang},
journal= {arXiv preprint arXiv:2501.15152},
year = {2025}
}