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Aspects of the numerical treatment of higher index DAEs

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

Abstract

This chapter sheds light on aspects of the direct numerical treatment of higher index DAEs. Not surprisingly, the integration methods approved for regular index-1 DAEs not longer perform well or fail, if they are applied in the same way to general higher index DAEs. We demonstrate various troubles, e.g., when integrating linear index-3 DAEs. These instabilities and numerical difficulties are due to the ill-posed character of the DAE solutions with respect to perturbations. We do not report index reduction techniques and methods basically exploiting special structural peculiarities to counteract the difficulties, which are discussed by many other authors. We present a procedure for the practical calculation of the index and add a few remarks on consistent initialization in the higher index case. This is of importance for users of DAE solver packages since they usually require knowledge about the DAE index.

Keywords

Numerical Treatment Matrix Sequence Implicit Euler Method Variable Stepsize Tractability Index 
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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