The Monte Carlo method is a powerful tool for solving many problems in the applied sciences. This is a simple, versatile, and robust method but it may suffer from a lack of precision. For improving accuracy, one possibility is to replace the pseudo-random numbers with low discrepancy point sets: this is the principle of quasi-Monte Carlo (QMC) methods.
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.