Fast and Slow Dynamics for the Computational Singular Perturbation Method

The Computational Singular Perturbation CSP method of Lam and Goussis is an iterative method to reduce the dimensionality of systems of ordinary di erential equations with multiple time scales In J Nonlin Sci to appear the authors showed that each iteration of the CSP algorithm improves the approxima tion of the slow manifold by one order In this paper it is shown that the CSP method simultaneously approximates the tangent spaces to the fast bers along which solutions relax to the slow manifold Again each iteration adds one order of accuracy In some studies the output of the CSP algorithm is postprocessed by linearly projecting initial data onto the slow manifold along these approximate tangent spaces These projections in turn also become successively more accurate AMS Subject Classi cation Primary C A C Secondary E E A