The index and split forms of linear differential-algebraic equations
type: Item
instance of: scholarly article
title: The index and split forms of linear differential-algebraic equations
zbMATH Open document ID: 1442.34031
DOI: 10.26516/1997-7670.2019.28.21
publication date: 2019-09-17T00:00:00Z
full work available at URL: http://mathizv.isu.ru/en/article/file
review text: Differential-algebraic equations (DAEs) composed by linear systems of ordinary differential equations (ODE) with rectangular matrices of coefficients are considered, including the case when the matrix before the derivative of the desired vector function has not full rank for all argument values from the domain. Criteria for the existence of nonsingular transformations splitting the system into subsystems are obtained, whose solution can be written down analytically using generalized inverse matrices. The resulting solution formula is called a generalized split form of a DAE and can be viewed as a certain analogue of the Weierstrass-Kronecker canonical form. In particular, it is shown that arbitrary DAEs with rectangular coefficient matrices are locally reducible to a generalized split form.
reviewed by: Yuqiang Feng
Mathematics Subject Classification ID: 34A09
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 34C20
zbMATH DE Number: 7105751
zbMATH Keywords: differential-algebraic equations
zbMATH Keywords: canonical form
zbMATH Keywords: split form
zbMATH Keywords: solution space
zbMATH Keywords: index
zbMATH Keywords: singular points
author: Mikhail Valer'yanovich Bulatov
author: V. F. Chistyakov
MaRDI profile type: Publication
OpenAlex ID: W2950799632
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Wikidata QID: Q127648358
published in: The Bulletin of Irkutsk State University. Series Mathematics
description: scientific article