Advances in Differential Equations

Exponentially accurate balance dynamics

D. Wirosoetisno

Full-text: Open access

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 ${\varepsilon}$).

Article information

Source
Adv. Differential Equations, Volume 9, Number 1-2 (2004), 177-196.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867972

Mathematical Reviews number (MathSciNet)
MR2099610

Zentralblatt MATH identifier
1120.34040

Subjects
Primary: 34E15: Singular perturbations, general theory
Secondary: 34E05: Asymptotic expansions 76M45: Asymptotic methods, singular perturbations 86A10: Meteorology and atmospheric physics [See also 76Bxx, 76E20, 76N15, 76Q05, 76Rxx, 76U05]

Citation

Wirosoetisno, D. Exponentially accurate balance dynamics. Adv. Differential Equations 9 (2004), no. 1-2, 177--196. https://projecteuclid.org/euclid.ade/1355867972


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