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

Chung, Y.-M.; Jolly, M.

doi:10.1090/S0025-5718-2014-02904-9

A unified approach to compute foliations, inertial manifolds, and tracking solutions
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by Y.-M. Chung and M. S. Jolly PDF

Math. Comp. 84 (2015), 1729-1751 Request permission

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 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.

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