Physics – Computational Physics
Scientific paper
2004-05-14
Physics
Computational Physics
21 pages, 1 figure
Scientific paper
The long-term dynamics of many dynamical systems evolve on an attracting, invariant "slow manifold" that can be parameterized by a few observable variables. Yet a simulation using the full model of the problem requires initial values for all variables. Given a set of values for the observables parameterizing the slow manifold, one needs a procedure for finding the additional values such that the state is close to the slow manifold to some desired accuracy. We consider problems whose solution has a singular perturbation expansion, although we do not know what it is nor have any way to compute it. We show in this paper that, under some conditions, computing the values of the remaining variables so that their (m+1)-st time derivatives are zero provides an estimate of the unknown variables that is an mth-order approximation to a point on the slow manifold in sense to be defined. We then show how this criterion can be applied approximately when the system is defined by a legacy code rather than directly through closed form equations.
Gear William C.
Kaper Tasso J.
Kevrekidis Ioannis G.
Zagaris Antonios
No associations
LandOfFree
Projecting to a Slow Manifold: Singularly Perturbed Systems and Legacy Codes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Projecting to a Slow Manifold: Singularly Perturbed Systems and Legacy Codes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Projecting to a Slow Manifold: Singularly Perturbed Systems and Legacy Codes will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-671916