The so-called anomalous fast diffusion in metallic alloys and semi-conductors is often analysed within an interstitial-substitutional model. The equations used for modelling these mechanisms are reaction-diffusion type whose analytical solutions are available only under drastic simplifications. The dissociative variety of this model is simulated using both finite difference (FD) and Monte Carlo (MC) methods. In MC simulation, diffusion of different species (interstitial impurities B-j, substitutional B-s, and vacancies V) and reaction jumps occur according to the suitable probabilities which are jump frequencies-dependent. Whereas in FD method, an implicit scheme is used to solve the system of non-linear partial differential equations. In both cases, the finite source conditions have been considered. A good agreement between results obtained by the two methods is found. On the other hand, the double-stages of simulated profiles are found to have similar shapes to those obtained experimentally in Nb(Co) and in GaAs(Zn). The first stage is well analysed by a Gaussian function, whereas the second one is well represented by an erfc type function. Furthermore, a detailed study of the two stages leads to a qualitative agreement with Stolwijk's analysis in two limited cases when the diffusion is vacancy- or foreign interstitial-controlled. However, the effective diffusion coefficients present a quantitative departure from those obtained by Stolwijk's expressions.