Laguerre approximation of stable manifolds with application to connecting orbits

Moore, Gerald

doi:10.1090/S0025-5718-03-01535-7

Laguerre approximation of stable manifolds with application to connecting orbits
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by Gerald Moore;

Math. Comp. 73 (2004), 211-242

DOI: https://doi.org/10.1090/S0025-5718-03-01535-7

Published electronically: April 22, 2003

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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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