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2004 Exponentially accurate balance dynamics
D. Wirosoetisno
Adv. Differential Equations 9(1-2): 177-196 (2004). DOI: 10.57262/ade/1355867972

Abstract

By explicitly bounding the growth of terms in a singular perturbation expansion with a small parameter ${\varepsilon}$, we show that it is possible to find a solution that satisfies a balance relation (which defines the slow manifold) up to an error that scales exponentially in ${\varepsilon}$ as ${\varepsilon}\to0$. This is first done for a generic finite-dimensional dynamical system with polynomial nonlinearity, followed by a continuous fluid case. In addition, for the finite-dimensional system, we show that, properly initialized, the solution of the full model stays within an exponential distance to that of the balance equation (i.e., evolution on the slow manifold) over a timescale of order one (independent of ${\varepsilon}$).

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D. Wirosoetisno. "Exponentially accurate balance dynamics." Adv. Differential Equations 9 (1-2) 177 - 196, 2004. https://doi.org/10.57262/ade/1355867972

Information

Published: 2004
First available in Project Euclid: 18 December 2012

zbMATH: 1120.34040
MathSciNet: MR2099610
Digital Object Identifier: 10.57262/ade/1355867972

Subjects:
Primary: 34E15
Secondary: 34E05 , 76M45 , 86A10

Rights: Copyright © 2004 Khayyam Publishing, Inc.

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Vol.9 • No. 1-2 • 2004
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