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Differential-Algebraic Equations (WS 2016/17)


Lecturer: Lena Scholz

Lecture: Mon 10-12  (MA 142),  Thu 12-14 (MA 750)

Office hours: Mon 12-14 (MA 463)


Topics of the lecture:

Differential-algebraic equations (DAEs) are essential tools in the modeling of dynamical processes. For example, the dynamical behaviour of mechanical systems, electrical circuits, flow problems, instationary heat transfer, elasticity problems, electromagnetic phenomena, or chemical reactions is often described by DAEs. While the analysis for ordinary differential equations is well developed, the situation regarding DAEs is more challenging and more complex. DAEs in general are not well suited for a direct numerical treatment using numerical ODE methods. One of the major difficulties lies in the existence of so called hidden constraints, i.e., algebraic restrictions which have to be satisfied for every solution.

In this lecture we will discuss

  • the analytical and numerical properties of DAEs,
  • several index concepts for the analysis of DAEs,
  • regularization approaches,
  • numerical integration of DAEs.



  • Lecture on Nov 14th, 2016: proof of canonical form (Slides)


Previous knowledge:

  • basic knowledge in the theory of ordinary differential equations and Linear Algebra
  • recommendable: basic knowledge in Numerical Analysis



  • P. Kunkel and V. Mehrmann. "Differential-Algebraic Equations: Analysis and Numerical Solution". EMS Publishing House Zürich 2006.
  • K. E. Brenan and S. L. Campbell and L. R. Petzold. "Numerical Solution of Initial-Value Problems in Differential Algebraic Equations" 2nd Ed. SIAM, Philadelphia, 1996 .
  • E. Hairer and C. Lubich and M. Roche. "The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods" Springer-Verlag, Berlin, 1989.
  • E. Hairer and G. Wanner. "Solving Ordinary Differential Equations II" 2nd Ed. Springer-Verlag, Berlin, 1996.




Dates for the oral exams:

  •     10.04.2017
  •     11.04.2017

Please register for the exam in the examination office (Prüfungsamt). After registration arrange the time for the exam in the office MA 4-5 (Mrs. Mokri). The confirmation of the registration ("gelber Zettel") is necessary.



1. Exercise

2. Exercise

3. Exercise

4. Exercise

5. Exercise

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