A flexible error estimate for the application of centre manifold theory

Li, Zhenquan and Roberts, A. J. (2007) A flexible error estimate for the application of centre manifold theory. Global Journal of Pure and Applied Mathematics, 3 (3). pp. 241-249. ISSN 0973-1768

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Abstract

In applications of centre manifold theory we need more flexible error estimates than that provided by, for example, the Approximation Theorem 3 by Carr [4, 6]. Here we extend the theory to cover the case where the order of approximation in parameters and that in dynamical variables may be completely different. This allows, for example, the effective evaluation of low-dimensional dynamical models at finite parameter values.

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Item Type:	Article (Commonwealth Reporting Category C)
Refereed:	Yes
Item Status:	Live Archive
Additional Information:	Submitted Version made accessible, and also available at http://arxiv.org/abs/math.DS/0002138
Faculty/School / Institute/Centre:	Historic - Faculty of Sciences - Department of Maths and Computing (Up to 30 Jun 2013)
Faculty/School / Institute/Centre:	Historic - Faculty of Sciences - Department of Maths and Computing (Up to 30 Jun 2013)
Date Deposited:	20 Apr 2010 12:32
Last Modified:	02 Jul 2013 23:48
Uncontrolled Keywords:	error; estimation theory; approximation theory; functional analysis; polynomials; centre manifold; error estimate
Fields of Research (2008):	01 Mathematical Sciences > 0101 Pure Mathematics > 010109 Ordinary Differential Equations, Difference Equations and Dynamical Systems 09 Engineering > 0915 Interdisciplinary Engineering > 091501 Computational Fluid Dynamics 01 Mathematical Sciences > 0101 Pure Mathematics > 010199 Pure Mathematics not elsewhere classified
Fields of Research (2020):	49 MATHEMATICAL SCIENCES > 4904 Pure mathematics > 490409 Ordinary differential equations, difference equations and dynamical systems 40 ENGINEERING > 4012 Fluid mechanics and thermal engineering > 401204 Computational methods in fluid flow, heat and mass transfer (incl. computational fluid dynamics) 49 MATHEMATICAL SCIENCES > 4904 Pure mathematics > 490499 Pure mathematics not elsewhere classified
Socio-Economic Objectives (2008):	E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
URI:	http://eprints.usq.edu.au/id/eprint/7527

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