Stability of reaction fronts in random walk simulations

A model of propagating reaction fronts is given for simple autocatalytic reactions and the stability of the propagating reaction fronts are studied in several numerical experiments. The corresponding random walk simulations - extending of a recent algorithm - make possible the simultaneous treatment of moving particles. A systematic comparison with the standard deterministic simulations highlight the advantages of the present stochastic approach. The main favor of the random walk simulation is that the initial perturbation has no strong effect on the stability of the front unlike in deterministic cases