A unified approach to compute foliations, inertial manifolds, and tracking initial conditions
Numerical Analysis
2012-11-06 v1 Dynamical Systems
Abstract
Several algorithms are presented for the accurate computation of the leaves in the foliation of an ODE near a hyperbolic fixed point. They are variations of a contraction mapping method in [25] to compute inertial manifolds, which represents a particular leaf in the unstable foliation. Such a mapping is combined with one for the leaf in the stable foliation to compute the tracking initial condition for a given solution. The algorithms are demonstrated on the Kuramoto-Sivashinsky equation.
Keywords
Cite
@article{arxiv.1211.0768,
title = {A unified approach to compute foliations, inertial manifolds, and tracking initial conditions},
author = {Y. -M. Chung and M. S. Jolly},
journal= {arXiv preprint arXiv:1211.0768},
year = {2012}
}