Closeness of Solutions for Singularly Perturbed Systems via Averaging
Systems and Control
2018-09-24 v1
Abstract
This paper studies the behavior of singularly perturbed nonlinear differential equations with boundary-layer solutions that do not necessarily converge to an equilibrium. Using the average of the fast variable and assuming the boundary layer solutions converge to a bounded set, results on the closeness of solutions of the singularly perturbed system to the solutions of the reduced average and boundary layer systems over a finite time interval are presented. The closeness of solutions error is shown to be of order O(\sqrt(\epsilon)), where \epsilon is the perturbation parameter.
Keywords
Cite
@article{arxiv.1809.07887,
title = {Closeness of Solutions for Singularly Perturbed Systems via Averaging},
author = {Mohammad Deghat and Saeed Ahmadizadeh and Dragan Nesic and Chris Manzie},
journal= {arXiv preprint arXiv:1809.07887},
year = {2018}
}