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July  2005, 13(4): 1057-1067. doi: 10.3934/dcds.2005.13.1057

Numerical periodic orbits of neutral delay differential equations

Nicola Guglielmi 1, and  Christian Lubich 2,

1. 

Dipartimento di Matematica Pura e Applicata, Università de L'Aquila, I-67100 L'Aquila, Italy
2. 

Mathematisches Institut, Universität Tübingen, D-72076 Tübingen, Germany

Received  December 2004 Revised  April 2005 Published  August 2005

This paper deals with the long-time behaviour of numerical solutions of neutral delay differential equations that have stable hyperbolic periodic orbits. It is shown that Runge--Kutta discretizations of such equations have attractive invariant closed curves which approximate the periodic orbit with the full order of the method, in spite of the lack of a finite-time smoothing property of the flow.
Keywords: Neutral delay differential equations, periodic orbit, Runge–Kutta methods, numerical solution, attractive invariant curves..
Mathematics Subject Classification: 65L05.
Citation: Nicola Guglielmi, Christian Lubich. Numerical periodic orbits of neutral delay differential equations. Discrete & Continuous Dynamical Systems, 2005, 13 (4) : 1057-1067. doi: 10.3934/dcds.2005.13.1057
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