A unified approach to compute foliations, inertial manifolds, and tracking initial conditions
2012
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.
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