  Slow manifolds are important geometric structures in the state spaces of
dynamical systems with multiple time scales. This paper introduces an algorithm
for computing trajectories on slow manifolds that are normally hyperbolic with
both stable and unstable fast manifolds. We present two examples of bifurcation
problems where these manifolds play a key role and a third example in which
saddle-type slow manifolds are part of a traveling wave profile of a partial
differential equation. Initial value solvers are incapable of computing
trajectories on saddle-type slow manifolds, so the slow manifold of saddle type
(SMST) algorithm presented here is formulated as a boundary value method. We
take an empirical approach here to assessing the accuracy and effectiveness of
the algorithm.
