×

An improved computational method for sensitivity analysis: Green’s function method with ’AIM’. (English) Zbl 0469.65049


MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
93B35 Sensitivity (robustness)
80A30 Chemical kinetics in thermodynamics and heat transfer
34A55 Inverse problems involving ordinary differential equations

Citations:

Zbl 0056.341

Software:

GEAR; EISPACK; DIFSUB
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Tomovic, R., Sensitivity analysis of dynamic systems (1963), McGraw-Hill: McGraw-Hill Oxford
[2] Demiralp, M. and Rabitz, H. J. Chem. Phys.; Demiralp, M. and Rabitz, H. J. Chem. Phys.
[3] Koda, M., J. Comp. Phys., 30, 259 (1979)
[4] Tomovic, R.; Vokobratovic, M., General Sensitivity Theory (1972), Elsevier: Elsevier New York
[5] Dickinson, R. P.; Gelinas, R. J., J. Comp. Phys., 21, 123 (1976)
[6] Hwang, J. T., J. Chem. Phys., 69, 5180 (1978)
[7] Dougherty, E. P., J. Chem. Phys., 71, 1794 (1979)
[8] Dougherty, E. P.; Rabitz, H., Int. J. Chem. Kinetics, 11, 1237 (1979)
[9] Dougherty, E. P.; Rabitz, H., J. Chem. Phys., 72, 6571 (1980)
[10] Edelson, D. et al.; Edelson, D. et al.
[11] Hindmarsh, A. C.; Gear, C. W., Ordinary Differential Equations System Solver (1974), Lawrence Livermore Laboratory: Lawrence Livermore Laboratory New York, Dec.
[12] Gear, C. W., ACM Commun., 14, 176 (1971)
[13] Magnus, W., Comm. Pure Appl. Math., 7, 649 (1954)
[14] Pechukas, P.; Light, J. C., J. Chem. Phys., 44, 3897 (1966), See, for example
[15] Chan, S., J. Chem. Phys., 49, 86 (1968)
[16] Smith, L. N. et al.J. Comp. Phys.; Smith, L. N. et al.J. Comp. Phys.
[17] Gantmacher, F. R., The theory of matrices (1959), Chelsea Pub. Co. · Zbl 0085.01001
[18] Moler, C.; Van Loan, C., SIAM Rev., 20, 801 (1978), For a review of these methods, see
[19] Shuler, K. E., Phys. Fluids, 2, 442 (1959)
[20] Bellman, R., Introduction to matrix analysis (1960), McGraw-Hill: McGraw-Hill New York · Zbl 0124.01001
[21] Smith, B. T., Matrix eigensystem routines — EISPAK guide, (Lecture Notes in Computer Science, Vol. 6 (1976), Springer-Verlag: Springer-Verlag New York) · Zbl 0289.65017
[22] Garbow, B. S., Matrix eigensystem routines — EISPACK guide extension, (Lecture Notes in Computer Science, Vol. 51 (1977), Springer-Verlag: Springer-Verlag New York) · Zbl 0368.65020
[23] Hall, G.; Watt, J. W., Modern numerical methods for ordinary differential equations (1976), Clarendon Press: Clarendon Press New York · Zbl 0348.65064
[24] Peters, G.; Wilkinson, J. H., Num. Math., 16, 181 (1970)
[25] Moler, C. B.; Stewart, G. W., SIAM J. Numer. Anal., 10, 241 (1973)
[26] Kronsjö, L. J., Algorithms: their complexity and efficiency (1979), Wiley: Wiley Oxford · Zbl 0438.68001
[27] Gelinas, R. J.; Shewes-Cox, P. D., J. Phys. Chem., 81, 2468 (1977)
[28] Cukier, R. I., J. Chem. Phys., 59, 3873 (1973)
[29] Schaibly, J. H.; Chuler, K. E., J. Chem. Phys., 59, 3879 (1973)
[30] Cukier, R. I., J. Chem. Phys., 63, 1140 (1975)
[31] Cukier, R. I., J. Comp. Phys., 26, 1 (1978)
[32] Demiralp, M. and Rabitz, H. ‘Chemical kinetic functional sensitivity analysis: derived sensitivities and general applications’, submitted to J. Chem. Phys.; Demiralp, M. and Rabitz, H. ‘Chemical kinetic functional sensitivity analysis: derived sensitivities and general applications’, submitted to J. Chem. Phys.
[33] Hoffert, M. I.; Stewart, R. W., Astronaut. Aeuronaut., 13, 42 (1975)
[34] Layokun, S. K.; Slater, D. H., Ind. Eng. Chem., 18, 232 (1979)
[35] Gomer, R.; Kistiakowsky, G. B., J. Chem. Phys., 19, 85 (1951)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.