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Spectral Intervals for Differential-Algebraic Equations and their Numerical Approximation

Please always quote using this URN:urn:nbn:de:0296-matheon-4144
  • Lyapunov and exponential dichotomy spectral theory is extended from ordinary differential equations (ODEs) to nonautonomous differential-algebraic equations (DAEs). By using orthogonal changes of variables, the original DAE system is transformed into appropriate condensed forms, for which concepts such as Lyapunov exponents, Bohl exponents, exponential dichotomy and spectral intervals of various kinds can be analyzed via the resulting underlying ODE. Some essential differences between the spectral theory for ODEs and that for DAEs are pointed out. Numerical methods for computing the spectral intervals associated with Lyapunov and Sacker-Sell (exponential dichotomy) spectra are derived by modifying and extending those methods proposed for ODEs. Perturbation theory and error analysis are discussed, as well. Finally, some numerical examples are presented to illustrate the theoretical results and the properties of the numerical methods.

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Metadaten
Author:Linh Vu Hoang, Volker Mehrmann
URN:urn:nbn:de:0296-matheon-4144
Referee:Peter Deuflhard
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2007/09/14
Release Date:2007/08/09
Tag:
Institute:Technische Universität Berlin
MSC-Classification:34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Dxx Stability theory [See also 37C75, 93Dxx] / 34D08 Characteristic and Lyapunov exponents
34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Dxx Stability theory [See also 37C75, 93Dxx] / 34D09 Dichotomy, trichotomy
65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L07 Numerical investigation of stability of solutions
65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L80 Methods for differential-algebraic equations
Preprint Number:402
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