Singular perturbation theory

When we apply the steady-state approximation (SSA) in chemi cal k netics, we typically argue that some of the intermediates are highly reactive, so that they a r removed as fast as they are made. We then set the corresponding rates of change to zero. What we re saying is not that these rates are identically zero, of course, but that they are much small er than the other rates of reaction. The steady-state approximation is often surprisingly accu rate, but the classical arguments lack rigor and don’t lead to any satisfying mathematical general ization which can be used to improve on the approximation. There are two mathematical theories w hich build on the SSA and provide the required generalization: