Numerical Treatment of Inverse Problems in Chemical Reaction Kinetics

  • H. G. Bock
Part of the Springer Series in Chemical Physics book series (CHEMICAL, volume 18)

Abstract

Chemical reaction systems are certainly one of the most challenging scientific fields in which numerical and analytical methods for ordinary differential equations are used.

Keywords

Covariance Pyridine Assure Pentane Piperidine 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 8.1
    P. Zwaga: Private Communication (1977)Google Scholar
  2. 8.2
    H.G. Bock, K.J. Plitt: A superlinearly convergent algorithm for direct solution of constrained optimal control problems (to appear)Google Scholar
  3. 8.3
    J. Milstein: Fitting multiple trajectories simultaneously to a model of inducible enzyme synthesis. Math Biosci. 40, 175 (1978)CrossRefGoogle Scholar
  4. 8.4
    C.W. Gear: Numerical Initial Value Problems in Ordinary Differential Equations ( Prentice Hall, Englewood Cliffs 1971 )Google Scholar
  5. 8.5
    J.H. Bremermann: A method of unconstrained global optimization. Math Biosci. 9, 1 (1970)CrossRefGoogle Scholar
  6. 8.6
    H.G. Bock: Numerical solution of nonlinear multipoint boundary value problems with applications to optimal control. Z Angew Math Mech. 58, 407 (1978)CrossRefGoogle Scholar
  7. 8.7
    R. Bulirsch: “Die Mehrzielmethode zur numerischen Lösung von nichtlinearen Randwertproblemen und Aufgaben der Optimalen Steuerung,” Carl- Cranz-Gesellschaft: Tech. Rpt. (1971)Google Scholar
  8. 8.8
    J. Stoer, R. Bulirsch: Einführung in die Numerische Mathematik II (Springer, Berlin, Heidelberg, New York 1973 )Google Scholar
  9. 8.9
    P. Deuflhard: “Recent Advances in Multiple Shooting Techniques”, in Computational Techniques for Ordinary Differential Equations, ed. by L. Gladwell/Sayers ( Academic Press, New York 1980 ) p. 217Google Scholar
  10. 8.10
    H.G. Bock: A Multiple Shooting Method for Parameter Identification in Nonlinear Differential Equations, GAMM Conference, Brussels (1978)Google Scholar
  11. 8.11
    H.G. Bock: Numerical Solution of Parameter Estimation Problems by Boundary Value Solvers, Workshop on Numerical Methods for Boundary Value Problems, Vancouver, Lecture Notes Collection (1980)Google Scholar
  12. 8.12
    H.G. Bock: “Derivative Free Methods for Parameter Identification in Nonlinear Differential Equations”; Dissertation, Universität Bonn (1981)Google Scholar
  13. 8.13
    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. 1977, ed. by J. Stoer, Lecture Notes Control Inf. Sei. 7/2, 22 (1978)Google Scholar
  14. 8.14
    P. Deuflhard: A modified newton method for the solution of ill-conditioned systems of nonlinear equations with application to multiple shooting. Numer Math. 22, 289 (1974)CrossRefGoogle Scholar
  15. 8.15
    P. Deuflhard: In Optimization and Optimal Control, ed. by R. Bulirsch, W. Oettli, J. Stoer, Springer Lecture Notes in Mathematics, Vol.477 (Springer, Berlin, Heidelberg, New York 1975 ) p. 59Google Scholar
  16. 8.16
    J. Stoer: On the numerical solution of constrained least squares problems. SIAM J Numer Anal. 8 /2, 382 (1971)CrossRefGoogle Scholar
  17. 8.17
    P. Businger, G.H. Golub: Linear least squares solutions by house-holder transformations. Numer Math. 7, 269 (1965)CrossRefGoogle Scholar
  18. 8.18
    P. Deuflhard, W. Sautter: On rank-deficient pseudo-inverses. J Lin Alg Appl. 22, 91 (1980)CrossRefGoogle Scholar
  19. 8.19
    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
  20. 8.20
    R. Bulirsch, J. Stoer: Numerical treatment of ordinary differential equations by extrapolation methods. Numer Math 9, 1 (1966)CrossRefGoogle Scholar
  21. 8.21
    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)CrossRefGoogle Scholar
  22. 8.22
    R. Roth, M. Roth: Data unscrambling and the analysis of inducible enzyme synthesis. Math. Biosci. 5, 57 (1969)CrossRefGoogle Scholar
  23. 8.23
    F. Heinmets: Analog computer analysis of a model system for the induced enzyme synthesis. J Theor Bio. 6, 60 (1964)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heildelberg 1981

Authors and Affiliations

  • H. G. Bock

There are no affiliations available

Personalised recommendations