On the computation of inertial manifolds

C. Foias, M. S. Jolly, I. G. Kevrekidis, G. R. Sell, E. S. Titi

Research output: Contribution to journalArticlepeer-review

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Abstract

A modified Galerkin (the "Euler-Galerkin") algorithmj for the computational of inertial manifolds is described and applied to reaction diffusion and the Kuramoto-Sivashinsky (KS) equation. In the context of the (KS) equation, a low-dimensional Euler-Galerkin approximation (n = 3) is distinctly superior to the traditional Galerkin of the same dimension, and comparable to a traditional Galerkin of a much higher dimension (n = 16).

Original languageEnglish (US)
Pages (from-to)433-436
Number of pages4
JournalPhysics Letters A
Volume131
Issue number7-8
DOIs
StatePublished - Sep 5 1988

Bibliographical note

Funding Information:
An inertial manifold is a finite-dimensional, exponentially attracting, positively invariant Lipschitz This work was partially supported by NSF grants CBT-8707090, EET-8717787, DMS-8507784, and DMS-8501933, DOE grant DE-FG02-86ER25020, and the Applied and Computational Mathematics Pmgram/DARPA.

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