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Linear DAEs with variable coefficients

  • René Lamour
  • Roswitha März
  • Caren Tischendorf
Part of the Differential-Algebraic Equations Forum book series (DAEF)

Abstract

We characterize the class of regular linear DAEs with variable coefficients by means of admissible matrix function sequences and associated projector functions. We do not use derivative arrays; instead we generate the admissible matrix functions directly from the coefficients of the given DAE. The so-called tractability index as well as several characteristic values are attributed to each regular DAE, which generalizes the Kronecker index and the Kronecker structural data of constant matrix pencils. We provide a constructive decoupling of regular DAEs into an inherent regular ODE and a subsystem containing all differentiations. Then, with this background, a comprehensive linear DAE theory is provided, including qualitative flow properties and a rigorous description of admissible excitations. Moreover, relations to several canonical forms and other index notions are addressed.

Keywords

Matrix Function Projector Function Constant Rank Tractability Index High Index DAEs 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • René Lamour
    • 1
  • Roswitha März
    • 1
  • Caren Tischendorf
    • 2
  1. 1.Department of MathematicsHumboldt-University of BerlinBerlinGermany
  2. 2.Mathematical InstituteUniversity of CologneCologneGermany

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