A method for model reduction in nonlinear ODE systems is demonstrated through computational examples. The method does not require an implicit separation of time-scales in the fine dynamics to be effective. From the computational standpoint, the method has the potential of serving as a subgrid modeling tool. From the physical standpoint, it provides a model for interpreting and describing history dependence in coarse-grained response of an autonomous system.
@article{arxiv.math-ph/0412022,
title = {Model Reduction via Parametrized Locally Invariant Manifolds: Some Examples},
author = {Aarti Sawant and Amit Acharya},
journal= {arXiv preprint arXiv:math-ph/0412022},
year = {2007}
}