Numerical schemes for continuum models of reaction-diffusion systems subject to internal noise

We present numerical schemes to integrate stochastic partial differential equations which describe the spatio-temporal dynamics of reaction-diffusion problems under the effect of internal fluctuations. The schemes conserve the non-negativity of the solutions and incorporate the Poissonian nature of internal fluctuations at small densities, their performance being limited by the level of approximation of density fluctuations at small scales. We apply the schemes to two different aspects of the Reggeon model, namely, the study of its nonequilibrium phase transition and the dynamics of fluctuating pulled fronts. In the latter case, our approach allows us to reproduce microscopic properties quantitatively within the continuum model.