A quasi-Monte Carlo method for the coagulation equation

Abstract

We propose a quasi-Monte Carlo algorithm for the simulation of the continuous coagulation equation. The mass distribution is approximated by a finite number $N$ of numerical particles. Time is discretized and quasi-random points are used at every time step to determine whether each particle is undergoing a coagulation. Convergence of the scheme is proved when $N$ goes to infinity, if the particles are relabeled according to their increasing mass at each time step. Numerical tests show that the computed solutions are in good agreement with analytical ones, when available. Moreover, the error of the QMC algorithm is smaller than the error given by a standard Monte Carlo scheme using the same time step and number $N$ of numerical particles.