Towards Parameter Identification for Large Chemical Reaction Systems

  • U. Nowak
  • P. Deuflhard
Part of the Progress in Scientific Computing book series (PSC, volume 2)


A standard task in the modelling of chemical reaction systems (CRS) is the identification of rate constants in the kinetic equations from given experimental data — which is the often so-called inverse problem (IP) of chemical kinetics (as opposed to simulation, the direct problem). For sufficiently complex CRS, the modelling problem itself is already rather intricate. So there is a need for user-oriented software that allows the chemist to concentrate on the chemistry of his process under investigation. As a first step in this direction, simulation packages have been developed — such as FACSIMILE [5], CHEMKIN [15] or LARKIN [10,3].


Incompatibility Factor Complex Chemical Reaction System Sparse Matrix Technique Stiff Integrator Parameter Identification Technique 
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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  1. [1]
    L. Armijo: Minimization of functions having Lipschitz-continuous first partial derivatives. Pacific J.Math. 16, 1–3 (1966).MathSciNetMATHGoogle Scholar
  2. [2]
    G. Bader, P. Deuflhard: A Semi-Implicit Midpoint Rule for Stiff Systems of Ordinary Differential Equations. Numer.Math., to appear (1983).Google Scholar
  3. [3]
    G. Bader, U. Nowak, P. Deuflhard: An Advanced Simulation Package for Large Chemical Reaction Systems. In: Aiken (ed.): Stiff Computation. Oxford University Press (1983).Google Scholar
  4. [4]
    H.G. Bock: Numerical Treatment of Inverse Problems in Chemical Reaction Kinetics. In [12], p.102–125 (1981).Google Scholar
  5. [5]
    E.M. Chance, A.R. Curtis, I.P. Jones, CR. Kirby: FACSIMILE: a computer program for flow and chemistry simulation, and general initial value problems. Harwell, AERE Tech.Rep.R. 8775 (Dec.1977).Google Scholar
  6. [6]
    P. Deuflhard: A Relaxation Strategy for the Modified Newton Method. In: Buiirsch/ Oettli/ Stoer (ed.): Optimization and Optimal Control. Springer Lecture Notes 477, 59–73 (1975).Google Scholar
  7. [7]
    P. Deuflhard, V. Apostolescu: A Study of the Gauss-Newton Method for the Solution of Nonlinear Least Squares Problems. In: Frehse/ Pallaschke/ Trottenberg (ed.): Special Topics of Applied Mathematics. Amsterdam: North-Holland Publ., p. 129–150 (1980).Google Scholar
  8. [8]
    P. Deuflhard, G. Heindl: Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods. SIAM J.Numer.Anal. 16, 1–10 (1979).MathSciNetMATHCrossRefGoogle Scholar
  9. [9]
    P. Deuflhard, W. Sautter: On Rank-Deficient Pseudo-Inverses. J.Lin.Alg.Appl. 29, 91–111 (1980).MathSciNetMATHCrossRefGoogle Scholar
  10. [10]
    P. Deuflhard, G. Bader, U. Nowak: LARKIN — a software package for the numerical simulation of LARge systems arising in chemical reaction KINetics. In [12], p.38–55 (1981).Google Scholar
  11. [11]
    I.S. Duff, U. Nowak: On sparse matrix techniques in a stiff integrator of extrapolation type. Univ. Heidelberg, SFB 123: Tech.Rep. (1982).Google Scholar
  12. [12]
    K.H. Ebert, P. Deuflhard, W. Jäger (ed.): Modelling of Chemical Reaction Systems. Springer Series Chem.Phys. 18 (1981).Google Scholar
  13. [13]
    D. Garfinkel, B. Hess: Metabolic Control Mechanisms VII. A detailed computer model of the glycolytic pathway in ascites cells. J.Bio.Chem. 239, 971–983 (1954).Google Scholar
  14. [14]
    W.B. Gragg: On Extrapolation Algorithms for Ordinary Initial Value Problems. SIAM J. Numer. Anal. 2, 384–404 (1965).MathSciNetGoogle Scholar
  15. [15]
    R.J. Kee, J.A. Miller, T..H. Jefferson: CHEMKIN: A General-Purpose, Problem-Independent, Transportable, Fortran Chemical Kinetics Code Package. Sandia National Laboratories, Livermore: Tech.Rep. SAND80-8003 (1980)Google Scholar
  16. [16]
    R.S. Martin, G. Peters, J.H. Wilkinson: Symmetric Decomposition of a Positive Definite Matrix Numer. Math. 7, 362–383 (1965).MathSciNetMATHGoogle Scholar
  17. [17]
    H.G. Bock: Recent Advances in Parameter Identification Techniques for ODEs. These proceedings, Chap. 7 (1983)Google Scholar

Copyright information

© Birkhäuser Boston 1983

Authors and Affiliations

  • U. Nowak
  • P. Deuflhard

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