Reactive and reactive-diffusive time scales in stiff reaction-diffusion systems

Two different sets of time scales arising in stiff systems of reaction-diffusion PDEs are examined; the first due to the reaction term alone and the second due to the interaction of the reaction and diffusion terms, The fastest time scales of each set are responsible for the development of a low dimensional manifold, the characteristics of which depend on the set of time scales considered. The advantages and disadvantages of employing these two manifolds for the simplification of large and stiff systems of reaction-diffusion PDEs arc discussed. It is shown that the two approaches provide a non-stiff simplified system of similar accuracy. The approach based on the reaction time scales allows for a simpler construction of the simplified system, while that based on the reaction/diffusion time scales allows for a simpler time marching scheme.