Laguerre approximation of stable manifolds with application to connecting orbits

Authors:
Gerald Moore
Affiliations:
Department of Mathematics, Imperial College, Queen's Gate, London SW7 2BZ England
Venue:
Mathematics of Computation
Year:
2004

Citing 5
Cited 1

Polynomials for infinite-domain spectral elements

Journal of Computational Physics
Computational aspects of pseudospectral Laguerre approximations

Applied Numerical Mathematics
Numerical computation and continuation of invariant manifolds connecting fixed points

SIAM Journal on Numerical Analysis
The numerical computation of connecting orbits in dynamical systems: a rational spectral approach

Journal of Computational Physics
Geometric methods for computing invariant manifolds

Applied Numerical Mathematics - Special issue on numerical methods for ordinary differential equations

A Hermite spectral method for the computation of homoclinic orbits and associated functionals

Journal of Computational and Applied Mathematics

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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.