Stability of periodic solutions of index-2 differential algebraic systems

Journal of Mathematical Analysis and Applications

Volumn 279, Issue 2, 2003, Pages 475-494

  Lamour, René ^a   März, Roswitha ^a   Winkler, Renate ^a  

^a HUMBOLDT UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037845249     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-247X(03)00024-6     Document Type: Article

References (15)

1. C.W. Gear, G.K. Gupta, B.J. Leimkuhler, Automatic integration of Euler-Lagrange equations with constraints, J. Comput. Appl. Math. 12/13 (1985) 77-90.
2. E. Griepentrog, R. März, Differential-Algebraic Equations and Their Numerical Treatment, Teubner-Texte Math., Vol. 88, Teubner, Leipzig, 1986.
3. E.-H. Horneber, Analyse nichtlinearer RLCÜ - Netzwerke mit Hilfe der gemischten Potentialfunktion mit einer systematischen Darstellung der Analyse nichtlinearer dynamischer Netzwerke, Ph.D. thesis, Universität Kaiserslautern, FB: Elektrotechnik, 1976.
4. K.E. Brenan, S.L. Campell, L.R. Petzold, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, North-Holland, New York, 1989.
5. P. Lötstedt, L. Petzold, Numerical solution of nonlinear differential equations with algebraic constraints. I: Convergence results for backward differentiation formulas, Math. Comp. 46 (1986) 491-516.
6. R. März, Some new results concerning index-2 differential-algebraic equations, J. Math. Anal. Appl. 140 (1989) 177-199.
7. R. März, On linear differential-algebraic equations and linearizations, Appl. Numer. Math. 18 (1995) 267-292.
8. R. März, Criteria for the trivial solution of differential algebraic equations with small nonlinearities to be asymptotically stable, J. Math. Anal. Appl. 225 (1998) 587-607.
9. R. März, EXTRA-ordinary differential equations: Attempts to an analysis of differential-algebraic systems, Progr. Math. 168 (1998) 313-334.
10. R. Lamour, R. März, R. Winkler, Stability of periodic solutions of index-2 differential algebraic systems, Preprint 98-23, Humboldt-Universität, Berlin, 1998.
11. L.S. Pontryagin, Gewöhnliche Differentialgleichungen, Deutscher Verlag der Wissenschaften, Berlin, 1965.
12. R. Lamour, R. März, R.M.M. Mattheij, On the stability behaviour of systems obtained by index-reduction, J. Comput. Appl. Math. 56 (1994) 305-319.
13. R. Lamour, R. März, R. Winkler, How Floquet theory applies to index 1 differential algebraic equations, J. Math. Anal. Appl. 217 (1998) 372-394.
14. S. Reich, On the local qualitative behavior of differential-algebraic equations, Circuits Systems Signal Process. 14 (1995) 427-443.
15. C. Tischendorf, Solution of index-2 differential algebraic equations and its application in circuit simulation, Ph.D. thesis, Humboldt-Universität zu Berlin, 1996.