Computing inertial manifolds

James C. Robinson

doi:10.3934/dcds.2002.8.815

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2002, Volume 8, Issue 4: 815-833. Doi: 10.3934/dcds.2002.8.815

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Computing inertial manifolds

James C. Robinson^1,

1.
Mathematics Institute, University of Warwick, Coventry CV4 7AL

Received: February 28, 2001

Revised: February 28, 2002

Published: September 2002

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Abstract

This paper discusses two numerical schemes that can be used to approximate inertial manifolds whose existence is given by one of the standard methods of proof. The methods considered are fully numerical, in that they take into account the need to interpolate the approximations of the manifold between a set of discrete gridpoints. As all the discretisations are refined the approximations are shown to converge to the true manifold.

Keywords:

Inertial manifolds,
approximate inertial manifolds.

Mathematics Subject Classification: 35B40, 35K22, 65M12.

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