Discretizing hyperbolic periodic orbits of delay differential equations

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

Volumn 83, Issue 1, 2003, Pages 38-49

  Farkas, Gyula ^a  

^a INSTITUTO SUPERIOR TÉCNICO   (Portugal)

Author keywords

Delay equation; Discretization; Periodic orbit

Indexed keywords

EID: 21144452396     PISSN: 00442267     EISSN: 15214001     Source Type: Journal    
DOI: 10.1002/zamm.200310003     Document Type: Article

References (12)

1. F. Alouges and A. Debussche, On the discretization of a partial differential equation in the neighborhood of a periodic orbit, Numer. Math. 65, 143-175 (1993).
2. P. W. Bates, K. Lu, and C. Zeng, Existence and persistence of invariant manifolds for semiflows in Banach space, Mem. Amer. Math. Soc. 135 (1998).
3. W.-J. Beyn, On invariant closed curves for one-step methods, Numer. Math. 51, 103-122 (1987).
4. W.-J. Beyn, On the numerical approximation of phase portraits near stationary points, SIAM J. Numer. Anal. 24, 1095-1113 (1987).
5. T. Eirola, Invariant curves of one-step methods, BIT 28, 113-122 (1988).
6. B. M. Garay, Estimates in discretizing normally hyperbolic compact invariant manifolds of ordinary differential equations, Comp. Math. Applic. (to appear)
7. J. Hale and S. M. Verduyn Lunel, Introduction to Functional Differential Equations (Springer, New York, 1993).
8. J. Hale and J. Scheurle, Smoothness of bounded solutions of nonlinear evolution equations, J. Diff. Eqs. 56, 142-163 (1985).
9. K. In 't Hout and C. Lubich, Periodic orbits of delay differential equations under discretization, BIT 38, 72-91 (1998).
10. C. Lubich and A. Ostermann, Hopf bifurcation of reaction-diffusion and Navier-Stokes equations under discretization, Numer. Math. 81, 53-84 (1998).
11. A. M. Stuart and A. M. Humphries, Dynamical Systems and Numerical Analysis (Cambridge University Press, Cambridge, 1996).
12. M. Zennaro, Delay differential equations: Theory and numerics, in: Theory and Numerics of Ordinary and Partial Differential Equations, edited by M. Ainsworth, W. A. Light, and M. Marlette (Oxford University Press, Oxford, 1995), pp. 291-333.