A graph theoretic method for identifying implicit two-time-scale problems

In nonlinear problems of a physical origin it is not unusual to derive system equations in coupled differential and algebraic subsets. A manifestation of the uncooperative nature of these systems is that frequently an explicit solution of the algebraic equation is not obtainable. Since the algebraic problem is imbedded in a larger dynamics problem, we have chosen to recast the system in two-time-scale form. This reformulation is obtained by using a graph-based approach, which allows the identification of local algebraic constraints prior to derivation of the system equations. An attribute of the approach is its flexibility, in that it permits a variety of two-time-scale formulations. The somewhat complementary nature of this approach and that of singular perturbations is remarked.