Hidden discontinuities and parametric sensitivity calculations

SIAM Journal on Scientific Computing

Volumn 23, Issue 6, 2002, Pages 1861-1874

  Tolsma, John E ^a   Barton, Paul I ^a  

^a Massachusetts Institute of Technology Cambridge   (United States)

Author keywords

Automatic differentiation; DAEPACK; Differential algebraic equations; Hybrid discrete continuous simulation; Parametric sensitivity analysis; State events

Indexed keywords

CODES (SYMBOLS); COMPUTER SIMULATION; MATHEMATICAL TRANSFORMATIONS; PROBLEM SOLVING; SENSITIVITY ANALYSIS;

PARAMETRIC SENSITIVITY ANALYSIS;

DIFFERENTIAL EQUATIONS;

EID: 0036447620     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S106482750037281X     Document Type: Article

References (18)

1. A. Back, J. Guckenheimer, And M. Meyers, A dynamical simulation facility for hybrid systems, in Hybrid Systems, R.L. Grossman, Lecture Notes in Comput. Sci., 736, A. Nerode, A.P. Ravn, and H. Rischel, eds., Springer-Verlag, New York, 1993, pp. 255-267.
2. L.G. Birta, T.I. Ören, And K.L. Kettenis, A robust procedure for discontinuity handling in continuous system simulation, Trans. Soc. Comput. Sim., 2 (1985), pp. 189-205.
3. C. Bischof, A. Carle, G. Corliss, A. Griewank, And P. Hovland, ADIFOR - Generating derivative codes from Fortran prograras, Scientific Programming, 1 (1992), pp. 11-29.
4. K.E. Brenan, S.L. Campbell, And L.R. Petzold, Numerical Solution of Initial Value Problems in Differential-Algebraic Equations, SIAM, Philadelphia, PA, 1995.
5. M.B. Carver, Efficient integration over discontinuities in ordinary differential equation simulations, Math. Comput. Simulation, 20 (1978), pp. 190-196.
6. F.E. Cellier, Combined Continuous/Discrete System Simulation by Use of the Digital Computer: Techniques and Tools, Ph.D. thesis, Swiss Federal Institute of Technology, Zurich, Switzerland, 1979.
7. W.F. Feehery, J.E. Tolsma, And P.I. Barton, Efficient sensitivity analysis of large-scale differential-algebraic systems, Appl. Numer. Math., 25 (1997), pp. 41-54.
8. S. Galán, W.F. Feehery, And P.I. Barton, Parametric sensitivity functions for hybrid discrete/continuous systems, Appl. Numer. Math., 31 (1999), pp. 17-47.
9. C.W. Gear and O. Osterby, Solving ordinary differential equations with discontinuities, ACM Trans. Math. Software, 10 (1984), pp. 23-44.
10. A. Griewank, On automatic differentiation, in Mathematical Programming: Recent Developments and Applications, M. Iri and K. Tanabe, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands, 1989, pp. 83-108.
11. A. Criewank, Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, SIAM, Philadelphia, PA, 2000.
12. J.L. Hay And A.W.J. Griffin, Simulation of discontinuous dynamical systems, in Proceedings of the 9th IMACS Conference on Simulation of Systems, 1979, L. Dekker, G. Savastano, and G.C. Vansteenkiste, eds., North-Holland, Amsterdam, 1980, pp. 79-87.
13. M. Kiehl, Sensitivity Analysis of ODEs and DAEs-Theory and Implementation Guide, Technical Report TUM-M9801, TUM Fakultät Für Mathematik, Munich, Germany, 1998.
14. T. Maly And L.R. Petzold, Numerical methods and software for sensitivity analysis of differential-algebraic systems, Appl. Numer. Math., 20 (1996), pp. 57-79.
15. T. Park And P.I. Barton, State event location in differential algebraic models, ACM Trans. Model. Comput. Sim., 6 (1996), pp. 137-165.
16. L.B. Rall, Automatic Differentiation: Techniques and Applications, Lecture Notes in Comput. Sci., 120, Springer-Verlag, Berlin, 1981.
17. J.E. Tolsma And P.I. Barton, DAEPACK: A Combined Symbolic and Numeric Library for General Numerical Calculations, Technical Report DAEPACK Web Page, Massachusetts Institute of Technology, Cambridge, MA, 2000.
18. J.E. Tolsma And P.I. Barton, DAEPACK: An open modeling environment for legacy models, Indust. Engrg. Chem. Res., 39 (2000), pp. 1826-1839.