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URN: urn:nbn:de:kobv:517-opus-15625
URL: http://opus.kobv.de/ubp/volltexte/2007/1562/

Ascher, Uri M. ; Chin, Hongsheng ; Reich, Sebastian

Stabilization of DAEs and invariant manifolds

Dokument 1.pdf (857 KB) (SHA-1:41a7496757012e06894b79158b2dcce9ec05cf64)

Kurzfassung auf Englisch

Many methods have been proposed for the stabilization of higher index differential-algebraic equations (DAEs). Such methods often involve constraint differentiation and problem stabilization, thus obtaining a stabilized index reduction. A popular method is Baumgarte stabilization, but the choice of parameters to make it robust is unclear in practice. Here we explain why the Baumgarte method may run into trouble. We then show how to improve it. We further develop a unifying theory for stabilization methods which includes many of the various techniques proposed in the literature. Our approach is to (i) consider stabilization of ODEs with invariants, (ii) discretize the stabilizing term in a simple way, generally different from the ODE discretization, and (iii) use orthogonal projections whenever possible. The best methods thus obtained are related to methods of coordinate projection. We discuss them and make concrete algorithmic suggestions.

Institut 1: Institut für Mathematik
Institut 2: Extern
DDC-Sachgruppe: Mathematik
Dokumentart: c Postprint
Schriftenreihe: Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe, ISSN 1866-8372
Band Nummer: paper 030
Sprache: Englisch
Erstellungsjahr: 1994
Publikationsdatum: 16.11.2007
first published in:
Numerische Mathematik - 67 (1994), 2, p. 131-149
ISSN: 0945-3245
doi: 10.1007/s002110050020
The original publication is available at www.springerlink.com.

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