zbMATH — the first resource for mathematics

Numerical methods and software for sensitivity analysis of differential-algebraic systems. (English) Zbl 0854.65056
The authors present some algorithms and software for sensitivity analysis of differential-algebraic equation systems. The algorithms have several novel features. The codes, which are extensions of DASSL and DASPK, are easy to use, highly efficient, and well suited for large scale problems.

65L05 Numerical methods for initial value problems
34A09 Implicit ordinary differential equations, differential-algebraic equations
34A34 Nonlinear ordinary differential equations and systems, general theory
65L07 Numerical investigation of stability of solutions
Full Text: DOI
[1] Bischof, C.; Carle, A.; Corliss, G.; Griewank, A.; Hovland, P., ADIFOR - generating derivative codes from Fortran programs, Sci. programming, 1, 11-29, (1992)
[2] Brenan, K.E.; Campbell, S.L.; Petzold, L.R., Numerical solution of initial-value problems in differential-algebraic equations, (1989), Elsevier Amsterdam · Zbl 0699.65057
[3] P.N. Brown, A.C. Hindmarsh and L.R. Petzold, Using Krylov methods in the solution of large-scale differential-algebraic systems, SIAM J. Sci. Comput. (to appear). · Zbl 0812.65060
[4] Caracotsios, M.; Stewart, W.E., Sensitivity analysis of initial value problems with mixed ODEs and algebraic equations, Comput. chem. engrg., 9, 359-365, (1985)
[5] Dennis, J.E.; Schnabel, R.B., Numerical methods for unconstrained optimization and nonlinear equations, (1983), Prentice-Hall Englewood Cliffs, NJ · Zbl 0579.65058
[6] Gill, P.E.; Murray, W.; Wright, M.H., Practical optimization, (1981), Academic Press New york · Zbl 0503.90062
[7] Haug, E.J.; Ehle, P.E., Second-order design sensitivity analysis of mechanical system dynamics, Internat. J. numer. methods engrg., 18, 1699-1717, (1982) · Zbl 0493.73085
[8] Haug, E.J.; Wehage, R.; Barman, N.C., Design sensitivity analysis of planar mechanism and machine dynamics, Trans. ASME, 103, (1981)
[9] Kramer, M.A.; Leis, J.R., The simultaneous solution and sensitivity analysis of systems described by ordinary differential equations, ACM trans. math. software, 14, 45-60, (1988) · Zbl 0639.65042
[10] R.S. Maier, L.R. Petzold and W. Rath, Parallel solution of large-scale differential-algebraic systems, in: Concurrency: Practice and Experience (to appear).
[11] Rabitz, H.; Kramer, M.; Dacol, D., Sensitivity analysis in chemical kinetics, Ann. rev. phys. chem., 34, 419-461, (1983)
[12] Saad, Y.P.; Schultz, M.H., A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. sci. statist. comput., 7, 856-869, (1986) · Zbl 0599.65018
[13] Tomovic, R.; Vukobratovic, M., General sensitivity theory, (1972), Elsevier New York · Zbl 0302.93014
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.