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QR Methods and Error Analysis for Computing Lyapunov and Sacker-Sell Spectral Intervals for Linear Differential-Algebraic Equations

Please always quote using this URN:urn:nbn:de:0296-matheon-6723
  • In this paper, we propose and investigate numerical methods based on QR factorization for computing all or some Lyapunov or Sacker-Sell spectral intervals for linear differential-algebraic equations. Furthermore, a perturbation and error analysis for these methods is presented. We investigate how errors in the data and in the numerical integration affect the accuracy of the approximate spectral intervals. Although we need to integrate numerically some differential-algebraic systems on usually very long time-intervals, under certain assumptions, it is shown that the error of the computed spectral intervals can be controlled by the local error of numerical integration and the error in solving the algebraic constraint. Some numerical examples are presented to illustrate the theoretical results.

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Metadaten
Author:Vu Hoang Linh, Volker Mehrmann, Erik Van Vleck
URN:urn:nbn:de:0296-matheon-6723
Referee:Peter Deuflhard
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2009/12/14
Release Date:2009/12/14
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:676
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