Identification of Rate Constants in Bistable Chemical Reactions

  • Johannes Schlöder
  • Hans Georg Bock
Part of the Progress in Scientific Computing book series (PSC, volume 2)


BELOUSOV [ 3] was the first to report on oscillating bromate oxidative reactions in 1958. Although isolated examples of oscillatory chemical reaction systems were known earlier, they were often ignored because such phenomena were considered to be ruled out by the second law of thermodynamics. In 1964, ZHABOTINSKII [24] exploited BELOUSOV’s investigations and discovered additional temporal and spatial effects.


Initial Guess Continuation Method Continuous Stir Tank Reactor Triangular Form Adjoint Variable 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    K. Bar-Eli, R.M. Noyes, J. Phys. Chem. 81, 1988 (1977)CrossRefGoogle Scholar
  2. [2]
    K. Bar-Eli, R.M. Noyes, J. Phys. Chem. 82, 1352 (1978)CrossRefGoogle Scholar
  3. [3]
    B.P. Belousov, Sborn. Referat. Rachats. Med., 1958, Medgiz, Moscow, 145 (1959)Google Scholar
  4. [4]
    H.G. Bock: A Multiple Shooting Method for Parameter Identification in Nonlinear Differential Equations, GAMM Conference, Brussels (1978)Google Scholar
  5. [5]
    H.G. Bock: Numerical Treatment of Inverse Problems in Chemical Reaction Kinetics, in [9]Google Scholar
  6. [6]
    H.G. Bock: Randwertproblemmethoden zur Parameteridentifizierung in Systemen nichtlinearer Differentialgleichungen (in preparation)Google Scholar
  7. [7]
    H.G. Bock: Recent Advances in Parameter Identification Techniques for O.D.E., these proceedingsGoogle Scholar
  8. [8]
    P. Businger, G.H. Golub: Linear Least Squares Solutions by Householder Transformations, Numer. Math. 7, 269 (1965)MathSciNetMATHCrossRefGoogle Scholar
  9. [9]
    K.H. Ebert, P. Deuflhard, W. Jäger (eds.): Modelling of Chemical Reaction Systems, Springer Series in Chemical Physics 18, Heidelberg (1981)Google Scholar
  10. [10]
    P. Deuflhard: A Modified Newton Method for the Solution of Ill-conditioned Systems of Nonlinear Equations with Applications to Multiple Shooting, Numer. Math. 22, 289 (1974)MathSciNetMATHCrossRefGoogle Scholar
  11. [11]
    P. Deuflhard: A Stepsize Control for Continuation Methods and its Application to Multiple Shooting, Numer. Math. 33, 115 (1979)MathSciNetMATHCrossRefGoogle Scholar
  12. [12]
    P. Deuflhard, V. Apostolescu: An Underrelaxed Gauss-Newton Method for Equality Constrained Nonlinear Least Squares Problems, in: Optimization Techniques, Proc. 8th IFiP Conf., Würzburg, Aug. 77, ed. by J. Stoer, Lecture Notes Control Inf. Sci., 7/2, 22 (1978)Google Scholar
  13. [13]
    P. Deuflhard, G. Bader: A Semi-implicit Mid-point Rule for Stiff Systems in Ordinary Differential Equations, SFB 123, Techn. Rep. 114, Univ. Heidelberg (1981)Google Scholar
  14. [14]
    P. Deuflhard, G. Bader, U. Nowak: LARKIN — A Software Package for the Numerical Simulation of Large Systems Arising in Chemical Reaction Kinetics, in [9]Google Scholar
  15. [15]
    P. Deuflhard, G. Heindl: Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods, SIAM J. Numer. Anal. 16/1, (1979)Google Scholar
  16. [16]
    R.J. Field, E. Körös, R.M. Noyes, J. Am. Chem. Soc. 94, 8649 (1972)CrossRefGoogle Scholar
  17. [17]
    W. Geiseler, K. Bar-Eli, J. Phys. Chem. 85, 908 (1981)CrossRefGoogle Scholar
  18. [18]
    W. Geiseler, H. Föllner, Biophys. Chem. 6, 107 (1977)CrossRefGoogle Scholar
  19. [19]
    J. Grievink, Koinklijke Shell-Laboratorium, Amsterdam, Private Communication (1981)Google Scholar
  20. [20]
    R.M. Noyes, R.J. Field, R.C. Thompson, J. Am. Chem. Soc. 93, 7315 (1971)CrossRefGoogle Scholar
  21. [21]
    V. Pereyra, H.B. Keller, W.H.K. Lee: Computational Methods for Inverse Problems in Geophysics: Inversion of Travel Time Observations, Phys. Earth Planet. Inter. 21, 120 (1980)CrossRefGoogle Scholar
  22. [22]
    Th. Reiners, Diploma Thesis (in preparation)Google Scholar
  23. [23]
    J. Swartz, J.H. Bremermann: Discussion of Parameter Estimation in Biological Modelling: Algorithms for Estimation and Evaluation of the Estimates, J. Math. Biol. 1, 241 (1975)MATHCrossRefGoogle Scholar
  24. [24]
    A.M. Zhabotinskii, Dokl. Akad. Nauk. SSSR 157, 392 (1964)Google Scholar

Copyright information

© Birkhäuser Boston 1983

Authors and Affiliations

  • Johannes Schlöder
  • Hans Georg Bock

There are no affiliations available

Personalised recommendations