Reverse Integration for Computing Stationary Points of Unstable Stiff Systems

Using existing, forward-in-time integration schemes, we demonstrate that it is possible to compute unstable, saddle-type fixed points of stiff systems of ODEs when the stable compenents are fast (i.e., rapidly damped) while the unstable components are slow. The approach has implications for the reverse (backward in time) integration of such stiff systems, and for the “coarse reverse” integration of microscopic/stochastic simulations.