This paper aims at the development of numerical schemes and simulation in a higher space dimension for nonlinear reaction diffusion problems with a convection that blows up in a finite time. A full discretization of this problem that preserves the blow up property is presented as well as a numerical simulation. We compare a speed of convergences of the Adomian decompositional method and the finite difference method.

full discretization, reaction diffusion equation, nonlinear parabolic problems, blow-up, finite difference, Adomian, simulation.