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Nowak, U.; Deuflhard, P.

Numerical identification of selected rate constants in large chemical reaction systems. (English) Zbl 0551.65051

Appl. Numer. Math. 1, 59-75 (1985).
Significant progress in the development of user-oriented software for parameter identification in large chemical reaction systems is reported. The progress includes new theoretical ideas and an increased domain of applicability of the codes. The solution of several realistic large scale problems is demonstrated.

Cited in 1 Review
Cited in 6 Documents

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
80A30 Chemical kinetics in thermodynamics and heat transfer
34A55 Inverse problems involving ordinary differential equations

Keywords:

stiff systems; rate coefficient; chemical mass action kinetics; parameter identification; large chemical reaction systems; realistic large scale problems

Software:

Larkin
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Full Text: DOI

References:

[1] Bader, G.; Deuflhard, P., A semi-implicit midpoint rule for stiff systems of ordinary differential equations, Numer. Math., 41, 373-398 (1983) · Zbl 0522.65050
[2] Bader, G.; Nowak, U.; Deuflhard, P., An advanced simulation package for large chemical reaction systems, (Tech. Rep. 149 (1982), Univer. Heidelberg). (Tech. Rep. 149 (1982), Univer. Heidelberg), Stiff Computation (1984), Oxford University Press: Oxford University Press Oxford, to appear
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[4] Bock, H. G., Recent advances in parameter identification techniques for ODE’s, (Deuflhard, P.; Hairer, E., Progress in Scientific Computing. Progress in Scientific Computing, Numerical Treatment of Inverse Problems in Differential and Integral Equations, 2 (1983), Birkhäuser: Birkhäuser Basel), 95-121 · Zbl 0516.65067
[5] Businger, P.; Golub, G. H., Linear least squares solutions by Householder transformations, Numer. Math., 7, 269-276 (1965) · Zbl 0142.11503
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[7] Deuflhard, P., A stepsize control for continuation methods and its special application to multiple shooting techniques, Numer. Math., 33, 115-146 (1979) · Zbl 0428.65032
[8] Deuflhard, P.; Sautter, W., On rank-deficient pseudoinverses, J. Lin. Alg. Appl., 29, 91-111 (1980) · Zbl 0452.65019
[9] Deuflhard, P.; Apostolescu, V., A study of the Gauss-Newton method for the solution of nonlinear least squares problems, (Frehse; Pallaschke; Trottenberg, Special Topics of Applied Mathematics (1980), North-Holland: North-Holland Amsterdam), 129-150 · Zbl 0443.65049
[10] Deuflhard, P.; Bader, G.; Nowak, U., LARKIN—a software package for the numerical simulation of Large systems arising in chemical reaction kinetics, (Ebert, K. H.; Deuflhard, P.; Jäger, W., Modelling of Chemical Reaction Systems. Modelling of Chemical Reaction Systems, Springer Ser. Chem. Phys., 18 (1981), Springer: Springer Berlin), 38-55
[11] Deuflhard, P., Recent progress in extrapolation methods for ODEs, (Tech. Rep. Nr. 224 (1983), Univ. Heidelberg), and, SIAM Rev., to appear · Zbl 0602.65047
[12] Garfinkel, D.; Hess, B., Metabolic control mechanisms. VII. A detailed computer model of the glycolytic pathway in ascites cells, J. Bio. Chem., 239, 971-983 (1964)
[13] Gear, C. W.; Vu, T., Smooth numerical solutions of ordinary differential equation systems, (Deuflhard, P.; Hairer, E., Progress in Scientific Computing. Progress in Scientific Computing, Numerical Treatment of Inverse Problems in Differential and Integral Equations, 2 (1983), Birkhäuser: Birkhäuser Basel), 2-12 · Zbl 0515.65058
[14] Isbarn, G., Kinetik, Mechanismus and Computersimulierung der thermischen Zersetzung von n-Hexan, (Dissertation (1981), Univ. Heidelberg., Inst. Phys. Chem)
[15] Isbarn, G.; Ederer, H. J.; Ebert, K. H., The thermal decomposition of n-hexane: kinetics, mechanism, and simulation, (Ebert, K. H.; Deuflhard, P.; Jäger, W., Springer Ser. Chem. Phys.. Springer Ser. Chem. Phys., Modelling of Chemical Reaction Systems, 18 (1981), Springer: Springer Berlin), 235-248
[16] Nowak, U.; Deuflhard, P., Towards parameter identification for large chemical reaction systems, (Deuflhard, P.; Hairer, E., Progress in Scientific Computing. Progress in Scientific Computing, Numerical Treatment of Inverse Problems in Differential and Integral Equations, 2 (1983), Birkhäuser: Birkhäuser Basel), 13-26 · Zbl 0549.65054
[17] F.W. Schneider, M. Heinrichs and T. Poll, Private communication, 1980.; F.W. Schneider, M. Heinrichs and T. Poll, Private communication, 1980.
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