Advances in Differential Equations

Exponentially accurate balance dynamics

D. Wirosoetisno

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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

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

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]


Wirosoetisno, D. Exponentially accurate balance dynamics. Adv. Differential Equations 9 (2004), no. 1-2, 177--196.

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