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Mathematics of Computation

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Laguerre approximation of stable manifolds with application to connecting orbits

Author: Gerald Moore
Journal: Math. Comp. 73 (2004), 211-242
MSC (2000): Primary 33C45, 37C29, 37M99, 65N35, 65P40
Published electronically: April 22, 2003
MathSciNet review: 2034118
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Abstract: We present an algorithm, based on approximation by Laguerre polynomials, for computing a point on the stable manifold of a stationary solution of an autonomous system. A superconvergence phenomenon means that the accuracy of our results is much higher than the usual spectral accuracy. Both the theory and the implementation of the method are considered. Finally, as an application of the algorithm, we describe a fully spectral approximation of homo- and heteroclinic orbits.

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Additional Information

Gerald Moore
Affiliation: Department of Mathematics, Imperial College, Queen’s Gate, London SW7 2BZ England

Keywords: Laguerre polynomials, invariant manifolds, homoclinic orbits, spectral methods
Received by editor(s): February 20, 2001
Received by editor(s) in revised form: May 13, 2002
Published electronically: April 22, 2003
Article copyright: © Copyright 2003 American Mathematical Society