Random-batch method for multi-species stochastic interacting particle systems

A random-batch method for interacting particle systems is proposed, extending the of S. Jin, L. Li, and J.-G. Liu (2020) [16] to multicomponent with without multiplicative noise. The idea algorithm randomly divide, at each time step, ensemble particles into small batches then evolve interaction within until next step. This reduces computational cost by one order magnitude, while keeping a certain accuracy. It proved that L2 error process behaves like square root step size, uniformly in time, thus providing convergence scheme. numerical efficiency tested some examples, simulations Poisson–Boltzmann model as well segregation two populations opinion formation hierarchical company are presented.