Nonstandard singular perturbation systems and higher index differential-algebraic systems.
type: Item
instance of: scholarly article
title: Nonstandard singular perturbation systems and higher index differential-algebraic systems.
zbMATH Open document ID: 1038.34002
DOI: 10.1016/S0096-3003(01)00288-0
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: Models of large-scale systems typically involve interacting dynamic phenomena of widely differing time-scales. These type of models may be treated as two time-scale singular perturbations systems (SPS), where the perturbation parameter is the ratio of the time-scales of the slow and fast dynamics. Tikhonov's theorem gives sufficient conditions on them to ensure a good approximation for a standard SPS, i.e., its corresponding slow system is a differential-algebraic system (DAS) of index 1. Here, it is shown that a nonstandard SPS with parameter set to zero can be seen as a DAS of higher index. This connection allows the authors to obtain a Tikhonov theorem when the DAS is of index 2.
Mathematics Subject Classification ID: 34A09
Mathematics Subject Classification ID: 34E15
zbMATH DE Number: 1861303
zbMATH Keywords: differential-algebraic systems
zbMATH Keywords: singular perturbations
author: Maria Etchechoury
author: Carlos H. Muravchik
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1861303