A unified approach to compute foliations, inertial manifolds, and tracking solutions. (English) Zbl 1347.37134
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 R. Rosa [Discrete Contin. Dyn. Syst. 1, No. 3, 421–448 (1995; Zbl 0883.34064)] 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.
MSC:
| 37M99 | Approximation methods and numerical treatment of dynamical systems |
| 34C45 | Invariant manifolds for ordinary differential equations |
Citations:
Zbl 0883.34064Software:
FOLI8PAKReferences:
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