  Eigenvalue analysis is a well-established tool for stability analysis of
dynamical systems. However, there are situations where eigenvalues miss some
important features of physical models. For example, in models of incompressible
fluid dynamics, there are examples where linear stability analysis predicts
stability but transient simulations exhibit significant growth of infinitesimal
perturbations. This behavior can be predicted by pseudo-spectral analysis. In
this study, we show that an approach similar to pseudo-spectral analysis can be
performed inexpensively using stochastic collocation methods and the results
can be used to provide quantitative information about instability. In addition,
we demonstrate that the results of the perturbation analysis provide insight
into the behavior of unsteady flow simulations.
