FULLY DISCRETE STABILITY AND INVARIANT RECTANGULAR REGIONS FOR REACTION-DIFFUSION SYSTEMS.

Reaction-diffusion systems are considered for which the range of the initial datum is confined to a rectangular slab, on the boundary of which the reactive vector field is inward pointing. Using the variational formulation of these partial differential equations as a starting point, we may define fully discrete analogues via finite differences, provided gradient approximations and quadratures are compatibly selected. It is determined herein that such discretizations are stable, i. e. , the evolution of the discrete approximation vectors is confined to the invariant slab. The boundary conditions considered are those suited for the applications to chemically reacting and biological systems.