Coarse-Graining Autonomous ODE Systems by Inducing a Separation of Scales: Practical Strategies and Mathematical Questions-Reference-Cited by-同舟云学术

Coarse-Graining Autonomous ODE Systems by Inducing a Separation of Scales: Practical Strategies and Mathematical Questions

Published:2009-03-11 Issue:3 Volume:15 Page:342-352
ISSN:1081-2865
Container-title:Mathematics and Mechanics of Solids
language:en
Short-container-title:Mathematics and Mechanics of Solids

Author:

Acharya Amit¹

Affiliation:

1. Department of Civil & Environmental Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA

Abstract

This short note introduces a methodology for sequential multiscale modeling of autonomous, “microscopic”, systems of Ordinary Differential Equations through a redefinition of the original dynamics as an augmented system with an explicit separation of time scales arising merely from the definition of time-averaging. Associated mathematical questions are stated and discussed.

Publisher

SAGE Publications

Subject

Mechanics of Materials,General Materials Science,General Mathematics

Link

http://journals.sagepub.com/doi/pdf/10.1177/1081286508100972

Reference12 articles.

1. Singularly perturbed ordinary differential equations with dynamic limits

2. Parametrized invariant manifolds: a recipe for multiscale modeling?

3. Model reduction via parametrized locally invariant manifolds: Some examples

4. On the Choice of Coarse Variables for Dynamics

5. On a computational approach for the approximate dynamics of averaged variables in nonlinear ODE systems: Toward the derivation of constitutive laws of the rate type

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