Hans Kaper
Argonne National Laboratory
Several methods have been proposed in the chemistry literature to reduce the dimension of systems of chemical kinetics equations with multiple time scales; we mention, among others, the equilibrium approximation, the (quasi-)steady state approximation, the ILDM method (Maas and Pope), the functional iteration method (Fraser and Roussel), and the CSP method (Goussis and Lam). These methods are being applied in practice, sometimes successfully, although their range of validity is not obvious and their accuracy is usually unknown. We have embarked on a mathematical analysis of some of these methods within the framework of dynamical systems theory and geometric singular perturbation theory. In this talk, I will focus on our results for the ILDM and CSP methods.