Index Determination in DAEs Using the Library indexdet and the ADOL-C Package for Algorithmic Differentiation

  • Dagmar Monett
  • René Lamour
  • Andreas Griewank
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 64)


We deal with differential algebraic equations (DAEs) with properly stated leading terms. The calculation of the index of these systems is based on a matrix sequence with suitably chosen projectors. A new algorithm based on matrices of Taylor polynomials for realizing the matrix sequence and computing the index is introduced. Derivatives are computed using algorithmic differentiation tools.


Differential algebraic equations tractability index ADOL-C 


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  1. 1.
    Bendtsen, C., Stauning, O.: FADBAD, a flexible C++ package for Automatic Differentiation. Tech. Rep. IMM–REP–1996–17, IMM, Dept. of Mathematical Modelling, Technical University of Denmark (1996)Google Scholar
  2. 2.
    Chang, Y.F., Corliss, G.F.: ATOMFT: Solving ODEs and DAEs using Taylor series. Computers & Mathematics with Applications 28, 209–233 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The John Hopkins University Press, Baltimore, MD, USA (1996)zbMATHGoogle Scholar
  4. 4.
    Griewank, A.: Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation. No. 19 in In Frontiers in Applied Mathematics. SIAM, Philadelphia, PA (2000)zbMATHGoogle Scholar
  5. 5.
    Hoefkens, J., Berz, M., Makino, K.: Efficient high-order methods for ODEs and DAEs. In: G. Corliss, F. Ch., A. Griewank, L. Hascoët, U. Naumann (eds.) Automatic Differentiation of Algorithms: From Simulation to Optimization, Computer and Information Science, chap. 41, pp. 343–348. Springer, New York, NY (2002)Google Scholar
  6. 6.
    König, D.: Indexcharakterisierung bei nichtlinearen Algebro-Differentialgleichungen. Master’s thesis, Institut für Mathematik, Humboldt-Universität zu Berlin (2006)Google Scholar
  7. 7.
    Lamour, A.: Index Determination and Calculation of Consistent Initial Values for DAEs. Computers and Mathematics with Applications 50, 1125–1140 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    März, R.: The index of linear differential algebraic equations with properly stated leading terms. In: Result. Math., vol. 42, pp. 308–338. Birkhäuser Verlag, Basel (2002)Google Scholar
  9. 9.
    März, R.: Differential Algebraic Systems with Properly Stated Leading Term and MNA Equations. In: K. Antreich, R. Bulirsch, A. Gilg, P. Rentrop (eds.) Modeling, Simulation and Optimization of Integrated Circuits, International Series of Numerical Mathematics, vol. 146, pp. 135–151. Birkhäuser Verlag, Basel (2003)Google Scholar
  10. 10.
    März, R.: Fine decoupling of regular differential algebraic equations. In: Result. Math., vol. 46, pp. 57–72. Birkhäuser Verlag, Basel (2004)Google Scholar
  11. 11.
    Nedialkov, N., Pryce, J.: Solving Differential-Algebraic Equations by Taylor Series (I): Computing Taylor coefficients. BIT Numerical Mathematics 45, Springer (2005)Google Scholar
  12. 12.
    Nedialkov, N., Pryce, J.: Solving Differential-Algebraic Equations by Taylor Series (II): Computing the System Jacobian. BIT Numerical Mathematics 47, Springer (2007)Google Scholar
  13. 13.
    Nedialkov, N., Pryce, J.: Solving Differential-Algebraic Equations by Taylor Series (III): the DAETS Code. Journal of Numerical Analysis, Industrial and Applied Mathematics 1(1), Springer (2007)Google Scholar
  14. 14.
    Pryce, J.D.: A Simple Structural Analysis Method for DAEs. BIT 41(2), 364–294 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Walther, A., Kowarz, A., Griewank, A.: ADOL-C: A Package for the Automatic Differentiation of Algorithms Written in C/C++, Version 1.10.0 (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Dagmar Monett
    • 1
  • René Lamour
    • 2
  • Andreas Griewank
    • 2
  1. 1.DFG Research Centre MATHEONHumboldt-Universität zu BerlinBerlinGermany
  2. 2.Institute of MathematicsHumboldt-Universität zu BerlinBerlinGermany

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