Nonstandard singular perturbation systems and higher index differential-algebraic systems

Autor:	Carlos H. Muravchik, María del Rosario Etchechoury
Rok vydání:	2003
Předmět:	Tikhonov regularization Computational Mathematics Algebraic equation Singular perturbation Differential equation Applied Mathematics Mathematical analysis Zero (complex analysis) Existence theorem Differential algebraic equation Implicit function theorem Mathematics
Zdroj:	Applied Mathematics and Computation. 134:323-344
ISSN:	0096-3003
DOI:	10.1016/s0096-3003(01)00288-0
Popis:	In order to obtain trajectory approximation results for a given singular perturbation system (SPS), two systems are derived from it: the slow and the fast one. 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. In this paper it is shown that a nonstandard SPS with the parameter set to zero can be seen as a DAS of higher index. This connection allows us to obtain a Tikhonov's theorem when this DAS is of index 2.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::2fa41cae640645cdbd609ed3242dd458 https://doi.org/10.1016/s0096-3003(01)00288-0 Zobrazit plný text záznamu Full Text from ScienceDirect