# A Simple Structural Analysis Method for DAEs

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## Abstract

We describe a straightforward method for analysing the structure of a differential-algebraic system. It generalizes the method of Pantelides, but is more directly informative and applies to DAEs with derivatives of any order. It naturally leads to a numerical method for the initial value problem that combines projection and index reduction. We illustrate the method by examples, and justify it with proofs. We prove that it succeeds on a fairly wide class of systems encountered in practice, and show its relation to the Pantelides method and to the Campbell-Gear derivative-array equations.

Assignment problems combinatorics differential algebraic equations index linear programming Taylor series

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## REFERENCES

- 1.D. P. Bertsekas,
*Linear Network Optimization*, MIT Press, London, 1991.Google Scholar - 2.K. E. Brenan, S. L. Campbell, and L. R. Petzold,
*Numerical Solution of Initial-value Problems in Differential-algebraic Equations*, North-Holland, New York, 1989.Google Scholar - 3.S. L. Campbell,
*Intelligent DAE solvers and user-friendly design, simulation and analysis packages*, in Proceedings of the IEEE International Conference on Systems, Manufacturing and Cybernetics, University of San Diego, 1998, pp. 3177–3182.Google Scholar - 4.S. L. Campbell and C. W. Gear,
*The index of general nonlinear DAEs*, Numer. Math., 72 (1995), pp. 173–196.Google Scholar - 5.Y. Chang and G. Corliss,
*ATOMFT: Solving ODEs and DAEs using Taylor series*, Comput. Math. Appl., 28 (1994), pp. 209–233.Google Scholar - 6.G. F. Corliss and Y. F. Chang,
*Solving ordinary differential equations using Taylor series*, ACM Trans. Math. Software, 8 (1982), pp. 114–144.Google Scholar - 7.I. S. Duff and C. W. Gear,
*Computing the structural index*, SIAM J. Algebraic Discrete Methods, 7 (1986), pp. 594–603.Google Scholar - 8.A. Griewank,
*On automatic differentiation*, in Mathematical Programming: Recent Developments and Applications, M. Iri and K. Tanabe, eds., Kluwer Academi Publishers, Dordrecht, 1989, pp. 83–108.Google Scholar - 9.S. E. Mattsson and G. Söderlind,
*Index reduction in differential-algebraic equations using dummy derivatives*, SIAM. J. Sci. Comput., 14 (1993), pp. 677–692.Google Scholar - 10.C. C. Pantelides,
*The consistent initialization of differential-algebraic systems*, SIAM. J. Sci. Stat. Comput., 9 (1988), pp. 213–231.Google Scholar - 11.J. D. Pryce,
*Solving high-index DAEs by Taylor series*, Numer. Algorithms, 19 (1998), pp. 195–211; Proceedings of Workshop on DAEs, Grenoble 1997.Google Scholar - 12.P. J. Rabier and W. C. Rheinboldt,
*A general existence and uniqueness theory for implicit differential-algebraic equations*, Differential Integral Equations, 4 (1991), pp. 553–582.Google Scholar - 13.G. Reiβig, 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 (2000), pp. 1987–1990.Google Scholar

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© Swets & Zeitlinger 2001