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Stabilization of DAEs and invariant manifolds

  • 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.

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Author:Uri M. Ascher, Hongsheng Chin, Sebastian ReichORCiD
Series (Serial Number):Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (paper 030)
Document Type:Postprint
Year of Completion:1994
Publishing Institution:Universität Potsdam
Release Date:2007/11/16
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Extern / Extern
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Notes extern:
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.