Solution operator approximations for characteristic roots of delay differential equations

Applied Numerical Mathematics

Volumn 56, Issue 3-4 SPEC. ISS., 2006, Pages 305-317

  Breda, Dimitri ^a  

^a UNIVERSITY OF UDINE   (Italy)

Author keywords

Eigenvalue problem; Runge Kutta methods; Solution operator semigroup

Indexed keywords

APPROXIMATION THEORY; COMPUTATION THEORY; EIGENVALUES AND EIGENFUNCTIONS; LINEAR SYSTEMS; NUMERICAL ANALYSIS; PROBLEM SOLVING; RUNGE KUTTA METHODS;

EIGENVALUE PROBLEM; LINEAR AUTONOMOUS SYSTEMS; NUMERICAL TESTS; SOLUTION OPERATOR SEMIGROUP;

DIFFERENTIAL EQUATIONS;

EID: 33644627509     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2005.04.010     Document Type: Article

References (17)

1. D. Breda, Methods for numerical computation of characteristic roots for delay differential equations: experimental comparison, in: BIOCOMP2002: Topics in Biomathematics and Related Computational Problems at the Beginning of the Third Millennium, Vietri, Italy, 2002, Sci. Math. Jpn., 58 (2), pp. 377-388
2. D. Breda, The infinitesimal generator approach for the computation of characteristic roots for delay differential equations using BDF methods, Research Report RR2/2002, Department of Mathematics and Computer Science, Università di Udine, Italy, 2002
3. D. Breda, Collection of numerical tests on the computation of characteristic roots for delay differential equations, Research Report RR2/2002, Department of Mathematics and Computer Science, Università di Udine, Italy, 2002
4. D. Breda, S. Maset, and R. Vermiglio Computing the characteristic roots for delay differential equations IMA J. Numer. Anal. 24 1 2004 1 19
5. D. Breda, S. Maset, R. Vermiglio, Pseudospectral differencing methods for characteristic roots of delay differential equations, SIAM J. Sci. Comput. (2004), in press
6. J.B. Conway Functions of One Complex Variable second ed. Graduate Texts in Math. vol. 11 1978 Springer New York
7. O. Diekmann, S.A. van Gils, S.M. Verduyn Lunel, and H.O. Walther Delay Equations - Functional, Complex and Nonlinear Analysis Appl. Math. Sci. vol. 110 1995 Springer New York
8. K. Engelborghs, T. Luzyanina, and D. Roose Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL ACM Trans. Math. Software 28 1 2000 1 21
9. K. Engelborghs, T. Luzyanina, G. Samaey, DDE-BIFTOOL v. 2.00: A Matlab package for bifurcation analysis of delay differential equations, Report TW330, Department of Computer Science, K. U. Leuven, Belgium, 2001
10. K. Engelborghs, and D. Roose On stability of LMS methods and characteristic roots of delay differential equations SIAM J. Numer. Anal. 40 2 2002 629 650
11. K. Engelborghs, and D. Roose Numerical computation of stability and detection of Hopf bifurcations of steady-state solutions of delay differential equations Adv. Comput. Math. 10 3-4 1999 271 289
12. A. Fattouh, O. Sename, J.M. Dion, H ∞ controller and observer design for linear systems with point and distributed delays, in: Proceedings of 2nd IFAC Workshop on Linear Time Delay Systems, Ancona, Italy, 2000
13. J.K. Hale, and S.M. Verduyn Lunel Introduction to Functional Differential Equations Appl. Math. Sci. vol. 99 1993 Springer New York
14. J.D. Lambert Numerical Methods for Ordinary Differential Systems 1997 Wiley Chichester, UK
15. T. Luzyanina, K. Engelborghs, and D. Roose Computing stability of differential equations with bounded distributed delays Numer. Algorithms 34 1 2003 41 66
16. S.I. Niculescu Delay Effects on Stability: A Robust Control Approach Lecture Notes in Control and Inform. Sci. vol. 269 2003 Springer New York
17. J.P. Richard Time-delay systems: an overview of some recent advances and open problems Automatica 39 2003 1667 1694