Please use this identifier to cite or link to this item: http://dx.doi.org/10.14279/depositonce-14572
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Main Title: A flow-on-manifold formulation of differential-algebraic-equations
Author(s): Baum, Ann-Kristin
Type: Research Paper
URI: https://depositonce.tu-berlin.de/handle/11303/15799
http://dx.doi.org/10.14279/depositonce-14572
License: http://rightsstatements.org/vocab/InC/1.0/
Abstract: We derive a flow formulation of differential-algebraic equations (DAEs), implicit differen-tial equations whose dynamics are restricted by algebraic constraints. Using the framework ofderivatives arrays and the strangeness-index, we identify the systems that are uniquely solv-able on a particular set of initial values and thus possess a flow, the mapping that uniquelyrelates a given initial value with the solution through this point. The flow allows to studysystem properties like invariant sets, stability, monotonicity or positivity. For DAEs, theflow further provides insights into the manifold onto which the system is bound to and intothe dynamics on this manifold. Using a projection approach to decouple the differential andalgebraic components, we give an explicit representation of the flow that is stated in theoriginal coordinate space. This concept allows to study DAEs whose dynamics are restrictedto special subsets in the variable space, like a cone or the nonnegative orthant.
Subject(s): differential-algebraic equations
flow
flow on surface
dynamical systems
Issue Date: 25-Nov-2014
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: 2014, 37
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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