A unified approach to compute foliations, inertial manifolds, and tracking solutions

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 used by Ricardo Rosa in 1995 to compute inertial manifolds, which represents a particular leaf in the unstable fol...

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Bibliographic Details
Published in:Mathematics of computation 2015-07, Vol.84 (294), p.1729-1751
Main Authors: CHUNG, Y.-M., JOLLY, M. S.
Format: Article
Language:English
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Summary: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 used by Ricardo Rosa in 1995 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 tracking solutions. The algorithms are demonstrated on the Kuramoto-Sivashinsky equation.
ISSN:0025-5718
1088-6842
DOI:10.1090/S0025-5718-2014-02904-9