A random-batch method for multi-species interacting particle systems is proposed, extending the method of S. Jin, L. Li, and J.-G. Liu [J. Comput. Phys. 400 (2020), 108877]. The idea of the algorithmus is to randomly divide, at each time step, the ensemble of particles into small batches and then to evolve the interaction of each particle within the batches until the next time step. This reduces the computational cost by one order of magnitude, while keeping a certain accuracy. It is proved that the $L^2$ error of the error process behaves like the square root of the time step size, uniformly in time, thus providing the convergence of the scheme. The numerical efficiency is tested for some examples, and numerical simulations of the opinion dynamics in a hierarchical company, consisting of workers, managers, and CEOs, are presented.

翻译：提出了多物种相互作用粒子系统的随机批量方法,将S. Jin、L. Li和J. G. Liu[J. Comput. Phys. 400 (2020年),108877]的方法加以扩展。算法的设想是,在每一步将粒子的集合分解成小批量,然后在分批中使每个粒子的相互作用演变到下一个步骤。这将计算成本降低一个数量级,同时保持一定的准确性。事实证明,错误过程的2美元错误表现为时间步骤大小的平方根,在时间上一致,从而提供了方案的趋同。对一些实例进行了数字效率测试,并对由工人、管理人员和首席执行官组成的一个分级公司的意见动态进行了数字模拟。