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Main Title: Positivity characterization of nonlinear DAEs. Part I: A flow formular for linear and nonlinear DAEs using projections
Author(s): Baum, Ann-Kristin
Mehrmann, Volker
Type: Research Paper
Abstract: We present a closed solution formula for differential-algebraic equations (DAEs) that generalizes the concept of the flow to linear and nonlinear problems of arbitrary index. This flow is stated in the original coordinate system and thus allows to study coordinate depending properties like positivity, in particular. Embedded in the concept of the strangeness-index, we separate the differential and algebraic components by a projection approach and remodel a given DAE as a semi-explicit system. Exploiting the results found in [2], we solve this system and compute a closed solution formula. Verifying that this solution is unique defined by the original DAE and uniquely related with a given consistent initial values, we construct the flow associated with a DAE with regular strangeness-index.
Subject(s): differential-algebraic equations
ordinary differential equations
Issue Date: 13-Aug-2013
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 34A09 Implicit equations, differential-algebraic equations
37C10 Vector fields, flows, ordinary differential equations
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2013, 20
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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