Solving differential algebraic equations by taylor series (III): The DAETS code

Journal of Numerical Analysis, Industrial and Applied Mathematics

Volumn 3, Issue 1-2, 2008, Pages 61-80

  Nedialkov, Nedialko S ^a   Pryce, John D ^b  

^a MCMASTER UNIVERSITY   (Canada)

^b CRANFIELD UNIVERSITY   (United Kingdom)

Author keywords

Automatic differentiation; Differential algebraic equations (DAEs); Structural analysis; Taylor series

Indexed keywords

EID: 67349205394     PISSN: 17908140     EISSN: 17908159     Source Type: Journal    
DOI: None     Document Type: Article

References (29)

1. U. M. Ascher, Hongsheng Chin, and Sebastian Reich. Stabilization of DAEs and invariant manifolds. Numerische Mathematik, 67(2):131-149, 1994.
2. K. Brenan, S. Campbell, and L. Petzold. Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. SIAM, Philadelphia, second edition, 1996.
3. P. Bunus and P. Fritzon. Methods for structural analysis and debugging of Modelica models. In Proceedings of the 2nd International Modelica, Conference, pages 157-165. Deutsches Zentrum für Luft und Raumfahrt Oberpfaffenhofen, Germany, March 2002.
4. S. L. Campbell and C. W. Gear. The index of general nonlinear DAEs. Numerische Mathematik, 72:173-196, 1995.
5. Y. F. Chang and George F. Corliss. ATOMFT: Solving ODEs and DAEs using Taylor series. Comp. Math. Appl, 28:209-233, 1994.
6. A. L. Dulmage and N. S. Mendelsohn. Coverings of bipartite graphs. Canad. J. Math, 1958.
7. A. Griewank, D. Juedes, and J. Utke. ADOL-C, a package for the automatic differentiation of algorithms written in C/C++. ACM Trans. Math. Software, 22(2):131-167, June 1996.
8. E. Hairer, S. P. N0rsett, and G. Wanner. Solving Ordinary Differential Equations I. Nonstiff Problems. Springer-Verlag, second edition, 1991.
9. E. Hairer and G. Wanner. Solving Ordinary Differential Equations II. Stiff and Differential- Algebraic Problems. Springer Verlag, Berlin, 1991.
10. T. E. Hull and W. H. Enright. A structure for programs that solve ordinary differential equations. Technical Report 66, Department of Computer Science, University of Toronto, May 1974.
11. R. Jonker and A. Volgenant. A shortest augmenting path algorithm for dense and sparse linear assignment problems. Computing, 38:325-340, 1987. The assignment code is available at www.magiclogic.com/assignment.html.
12. A. Jorba and M. Zou. A software package for the numerical integration of ODEs by means of high-order Taylor methods. Technical report, Department of Mathematics, University of Texas at Austin, TX 78712-1082, USA, 2001.
13. S. E. Mattsson and G. Soüderlind. Index reduction in differential-algebraic equations using dummy derivatives. SIAM J. Sci. Comput., 14(3):677-692, 1993.
14. F. Mazzia and F. Iavernaro. Test set for initial value problem solvers. Technical Report 40, Department of Mathematics, University of Bari, Italy, 2003. http://pitagora.dm.uniba.it/~testset/.
15. N. S. Nedialkov and K. R. Jackson. The design and implementation of a validated object-oriented solver for IVPs for ODEs. Technical Report 6, Software Quality Research Laboratory, Department of Computing and Software, McMaster University, Hamilton, Canada, L8S 4K1, 2002.
16. N. S. Nedialkov and J. D. Pryce. Solving differential-algebraic equations by Taylor series (I): Computing Taylor coefficients. BIT, 45:561-591, 2005.
17. N. S. Nedialkov and J. D. Pryce. Solving differential-algebraic equations by Taylor series (III): The DAETS code. Technical report, Department of Computing and Software, McMaster University, Hamilton, Ontario, Canada, L8S 4K1, November 2007.
18. N. S. Nedialkov. Computing Rigorous Bounds on the Solution of an Initial Value Problem for an Ordinary Differential Equation. PhD thesis, Department of Computer Science, University of Toronto, Toronto, Canada, M5S 3G4, February 1999.
19. C. C. Pantelides. The consistent initialization of differential-algebraic systems. SIAM. J. Sci. Stat. Com/put., 9:213-231, 1988.
20. A. Pothen and C.-J. Fan. Computing the block triangular form of a sparse matrix. ACM Transactions on Mathematical Software, 16(4):303-324, December 1990.
21. LAPACK project. LAPACK - Linear Algebra PACKage. http://www.netlib.org/lapack/.
22. J. D. Pryce and N. S. Nedialkov. DAETS user guide. Technical report, Department of Computing and Software, McMaster University, Hamilton, Ontario, Canada, L8S 4K1, 2007.
23. J. D. Pryce. Solving high-index DAEs by Taylor Series. Numerical Algorithms, 19:195-211, 1998.
24. J. D. Pryce. A simple structural analysis method for DAEs. BIT, 41(2):364-394, 2001.
25. G. J. Reid, P. Lin, and A. D. Wittkopf. Differential-elimination completion algorithms for DAE and PDAE. Studies in Applied Mathematics, 106(1):1-45, December 2001.
26. G. Reissig, W. S. Martinson, and P. I. Barton. Differential-algebraic equations of index 1 may have an arbitrarily high structural index. SIAM J. Sci. Comput., 21(6):1987-1990, 1999.
27. O. Stauning and C. Bendtsen. FADBAD++ web page, May 2003. FADBAD++ is available at www.imm.dtu.dk/fadbad.html.
28. A. Wächter. An Interior Point Algorithm for Large-Scale Nonlinear Optimization with Applications in Process Engineering. PhD thesis, Carnegie Mellon University, Pittsburgh, PA, 2002.
29. L. T. Watson. A globally convergent algorithm for computing fixed points of C2 maps. Appl. Math. Comput., 5:297-311, 1979.