Differential-algebraic equations: A tutorial review

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 8, Issue 7, 1998, Pages 1399-1411

  Beardmore, R E ^a   Song, Y H ^a  

^a BRUNEL UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039504241     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127498001091     Document Type: Review

References (30)

1. Alscher, C. [1997] "A dynamic model of the leech," Ann. Num. Math. Differential-Algebraic Equations: Numerical and Formal Aspects, to appear.
2. Ambrosetti, A. & Prodi, G. [1992] A Primer of Nonlinear Analysis, Cambridge Studies in Advanced Mathematics, Vol. 34 (Cambridge University Press).
3. Beardmore, R. E. & Song, Y. H. [1998] "Singularity induced bifurcation, DAEs and power system models," Ann. Num. Math. Differential-Algebraic Equations: Numerical and Formal Aspects, to appear.
4. Brenan, K. E., Campbell, S. L. & Petzold, L. R. [1989] Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations (North Holland, Elsevier Science Publishing).
5. Byrne, G. D. & Ponzi, P. R. [1988] "Differential-algebraic systems, their applications and solutions," Comput. Chem. Eng. 12(5), 377-382.
6. Campbell, S., Hollenbeck, R. & Marszalek, W. [1998] "Mixed symbolic-numeric computations with general DAE," Ann. Num. Math. Differential-Algebraic Equations: Numerical and Formal Aspects, to appear.
7. Campbell, S. L. & Griepentrog, E. [1995] "Solvability of general differential-algebraic equations," SIAM J. Sci. Comput. 16(2), 257-270.
8. Campbell, S. L. & Marszalek, W. [1996] "The index of an infinite-dimensional implicit system," Report, North Carolina State University, Department of Mathematics.
9. Chua, L. O. [1989] "Impasse points. Part II. Analytical aspects," Int. J. Circuit Theor. Appl. 17, 271-282.
10. Chua, L. O. & Deng, A. C. [1989] "Impasse points. Part I. Numerical aspects," Int. J. Circuit Theor. Appl. 17, 213-235.
11. Coroian, D. I. [1994] "Existence and uniqueness for a class of delay DAEs," Preprint, University of Iowa.
12. Glendinning, P. [1996] Stability, Instability and Chaos, Cambridge Texts in Applied Mathematics (Cambridge University Press).
13. Grindrod, P. [1996] The Theory and Applications of Reaction-Diffusion Equations: Patterns and Waves, Oxford Applied Mathematics and Computing Science Series, 2nd edition (Oxford University Press).
14. Guan, Z.-H., Lui, Y.-Q. & Wen, X.-C. [1995] "Decentralized stabilization of singular and time-delay large-scale control systems with impulsive solutions," IEEE Trans. Automatic Control 40(8), 1437-1441.
15. Guckenheimer, J. & Holmes, P. [1986] Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (Springer-Verlag, NY).
16. Hill, D. J. & Mareels, I. M. Y. [1990] "Stability theory for DAES with application to power systems," IEEE CAS Part I 37(11), 1416-1423.
17. Kumer, A. & Daoutidis, P. [1997] "High index DAE systems in modeling and control of chemical processes," Control Ind. Syst. IFAC-IFIP-IMACS Conf. 20-22 May 1997, 518-523.
18. Kwatny, H. G., Fischl, R. F. & Nwankpa, C. O. [1995] "Local bifurcation in power systems: Theory, computation and application," Proc. IEEE 83(11), 1456-1483.
19. Le Vey, G. [1994] "Differential algebraic equations, a new look at the index," Internal publication no. 808, IRISA, Campus de Beaulieu, 35042 Rennes Cedex, France.
20. McPhee, J. J. [1996] "On the use of linear graph theory in multibody system dynamics," Nonlin. Dyn. 9, 73-90.
21. Petzold, L. [1982] "Differential algebraic equations are not ODEs," SIAM J. Sci. Stat. Comput. 3(3), 367-384.
22. Petzold, L. R. [1995] "Numerical solution of delay DAEs," SIAM J. Numer. Anal. 32(5), 1635-1657.
23. Rabier, P. J. & Rheinoldt, W. C. [1994] "On impasse points of quasilinear differential-algebraic equations," J. Math. Anal. Appl. 181, 429-454.
24. Rabier, P. J. & Rheinoldt, W. C. [1995] "Discontinuous solutions of semilinear DAEs-I distribution solutions," Nonlin. Anal. 27(11), 1241-1256.
25. Reich, S. [1995] "On the qualitative behavior of DAEs," Circuits Syst. Signal Process. 14(4), 427-443.
26. Simeon, B. [1998] "DAEs and PDEs in elastic multibody systems," Ann. Num. Math. Differential-Algebraic Equations: Numerical and Formal Aspects, to appear.
27. Venkatasubramanian, V. [1994] "Singularity induced bifurcation in the Van Der Pol oscillator," IEEE Trans. Circuits Syst. Part I: Fundamental Theor. Appl. 41(11), 765-769.
28. Venkatasubramanian, V., Schattier, H. & Zaborszky, J. [1992] "A stability theory of large differential algebraic systems. A taxonomy," No SSM 9201 Part 1. Technical report, Washington University, Washington, USA.
29. von Sosen, H. [1994] "Part I: Folds and bifurcations in the solutions of semi-explicit DAEs," PhD dissertation, Californian Institute of Technology, Pasadena, California.
30. Wiggins, S. [1990] Introduction to Applied Nonlinear Dynamical Systems and Chaos, Texts in Applied Mathematics. Vol. 2 (Springer-Verlag, NY).