Closeness of Solutions for Singularly Perturbed Systems via Averaging

2018/09/20 by Mohammad Deghat, Saeed Ahmadizadeh, Deghat, Mohammad +5
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #FOS: Electrical engineering #Nonlinear Differential Equations Analysis #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.1809.07887

openalex publication_date 2018/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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(√(ε)), where εis the perturbation parameter.

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