Abstract
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].
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
L. Armijo: Minimization of functions having Lipschitz-continuous first partial derivatives. Pacific J.Math. 16, 1–3 (1966).
G. Bader, P. Deuflhard: A Semi-Implicit Midpoint Rule for Stiff Systems of Ordinary Differential Equations. Numer.Math., to appear (1983).
G. Bader, U. Nowak, P. Deuflhard: An Advanced Simulation Package for Large Chemical Reaction Systems. In: Aiken (ed.): Stiff Computation. Oxford University Press (1983).
H.G. Bock: Numerical Treatment of Inverse Problems in Chemical Reaction Kinetics. In [12], p.102–125 (1981).
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).
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).
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).
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).
P. Deuflhard, W. Sautter: On Rank-Deficient Pseudo-Inverses. J.Lin.Alg.Appl. 29, 91–111 (1980).
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).
I.S. Duff, U. Nowak: On sparse matrix techniques in a stiff integrator of extrapolation type. Univ. Heidelberg, SFB 123: Tech.Rep. (1982).
K.H. Ebert, P. Deuflhard, W. Jäger (ed.): Modelling of Chemical Reaction Systems. Springer Series Chem.Phys. 18 (1981).
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).
W.B. Gragg: On Extrapolation Algorithms for Ordinary Initial Value Problems. SIAM J. Numer. Anal. 2, 384–404 (1965).
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)
R.S. Martin, G. Peters, J.H. Wilkinson: Symmetric Decomposition of a Positive Definite Matrix Numer. Math. 7, 362–383 (1965).
H.G. Bock: Recent Advances in Parameter Identification Techniques for ODEs. These proceedings, Chap. 7 (1983)
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1983 Birkhäuser Boston
About this chapter
Cite this chapter
Nowak, U., Deuflhard, P. (1983). Towards Parameter Identification for Large Chemical Reaction Systems. In: Deuflhard, P., Hairer, E. (eds) Numerical Treatment of Inverse Problems in Differential and Integral Equations. Progress in Scientific Computing, vol 2. Birkhäuser Boston. https://doi.org/10.1007/978-1-4684-7324-7_2
Download citation
DOI: https://doi.org/10.1007/978-1-4684-7324-7_2
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-3125-3
Online ISBN: 978-1-4684-7324-7
eBook Packages: Springer Book Archive