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A note on the uniform perturbation index

Arnold, M. (1998) A note on the uniform perturbation index. In: Rostocker Mathematisches Kolloquium, 52, pp. 33-46. DAE's Related Fields and Application.

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Abstract

For a given differential-algebraic equation (DAE) the perturbation index gives a measure for the sensitivity of a solution w.r.t. small perturbations. If we consider, however, classes of DAEs (e.g. all DAEs that arise as semi-discretizations of a given partial DAE by the method of lines) then the error bound in the definition of the perturbation index may become arbitrarily large even if the perturbation index does not exceed 1. We illustrate this fact by 2 examples and define as alternative the uniform perturbartion index that gives simultaneously error bounds for all DAEs of a fiven class. We prove that in one example each individual DAE has perturbation index 1 but the uniform perturbation index is 2. Another example illustrates that the class of all finite difference semi-discretizations may even have no uniform perturbation index if the given partial DAE has perturbation index 2.

Item URL in elib:https://elib.dlr.de/14169/
Document Type:Conference or Workshop Item (Speech)
Additional Information: LIDO-Berichtsjahr=2000,
Title:A note on the uniform perturbation index
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Arnold, M.UNSPECIFIEDUNSPECIFIED
Date:1998
Journal or Publication Title:Rostocker Mathematisches Kolloquium
Open Access:No
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
Volume:52
Page Range:pp. 33-46
Status:Published
Keywords:ifferential-algebraic equations, perturbation index, Baumgarte stabilization, partial DAEs, method of lines
Event Title:DAE's Related Fields and Application
HGF - Research field:other
HGF - Program:other
HGF - Program Themes:other
DLR - Research area:no assignment
DLR - Program:no assignment
DLR - Research theme (Project):UNSPECIFIED
Location: Göttingen
Institutes and Institutions:Institute of Aeroelasticity
Deposited By: DLR-Beauftragter, elib
Deposited On:16 Sep 2005
Last Modified:14 Jan 2010 21:30

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