Numerical treatment of retarded differential-algebraic equations by collocation methods

Advances in Computational Mathematics

Volumn 7, Issue 4, 1997, Pages 573-592

  Hauber, R ^a  

^a UNIVERSITY OF MUNICH   (Germany)

Author keywords

Collocation methods; Delay differential equations; Differential algebraic equations; State dependent lag

Indexed keywords

EID: 21744432249     PISSN: 10197168     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1018919508111     Document Type: Article

References (19)

1. U. Ascher and L.R. Petzold, The numerical solution of delay-differential-algebraic equations of retarded and neutral type, SIAM J. Numer. Anal. 32(5) (1995).
2. C.T.H. Baker and C. Paul, Parallel continuous Runge-Kutta methods and vanishing lag delay differential equations, Adv. Comput. Math. 1 (1993).
3. C.T.H. Baker, C. Paul and D.Willé, Issues in the numerical solution of evolutionary delay differential equations, Adv. Comput. Math. 3 (1995).
4. K.E. Brenan and L.R. Petzold, The numerical solution of higher index differential/algebraic equations by implicit methods, SIAM J. Numer. Anal. 26(4) (1989).
5. S.L. Campbell, Singular linear systems of differential equations with delay, Appl. Anal. 2 (1980).
6. S.L. Campbell, 2-D (differential-delay) implicit systems, in: Proc. IMACS World Congress on Scientific Computation, Dublin (1991).
7. S.L. Campbell, Nonregular descriptor systems with delays, in: Proc. Symposium on Implicit and Nonlinear Systems, Arlington, TX (December 1992).
8. A. Feldstein and K. Neves, High order methods for state-dependent delay differential equations with nonsmooth solutions, SIAM J. Numer. Anal. 21(5) (1984).
9. E. Hairer, C. Lubich and M. Roche, The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods, Lecture Notes in Mathematics 1409 (Springer, Berlin, 1989).
10. E. Hairer and G. Wanner, Solving Ordinary Differential Equations I (Springer, Berlin, 1987).
11. E. Hairer and G. Wanner, Solving Ordinary Differential Equations II (Springer, Berlin, 1991).
12. R. Hauber, Numerische Behandlung retardierter differential-algebraischer Gleichungen, Dissertation, München (1994).
13. H. Hayashi and W. Enright, Numerical algorithm for vanishing delay problems, in: Proc. 14th Annual Meeting of the Canadian Applied Mathematical Society, York University, Canada, May 30-June 2 (1993).
14. D. Higham, Error control for initial value problems with discontinuities and delays, Appl. Numer. Math. 12 (1993).
15. A. Karoui and R. Vaillancourt, Computer solutions of state-dependent delay differential equations, Comput. Math. Appl. 27(4) (1994).
16. K. Neves and A. Feldstein, Characterization of jump discontinuities for state-dependent delay differential equations, J. Math. Anal. Appl. 56 (1976).
17. C. Paul, Developing a delay differential equation solver, Appl. Numer. Math. 9 (1992).
18. W.C. Rheinboldt, On the existence and uniqueness of solutions of nonlinear semi-implicit differential-algebraic equations, Nonlinear Anal. 16(7/8) (1991).
19. D. Willé and C.T.H. Baker, The tracking of derivative discontinuities in systems of delay-differential equations, Appl. Numer. Math. 9 (1992).