Numerical periodic orbits of neutral delay differential equations
Nicola Guglielmi - Dipartimento di Matematica Pura e Applicata, Università de L'Aquila, I-67100 L'Aquila, Italy (email)
Abstract: 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, numerical solution,
Runge–Kutta methods, attractive invariant curves.
Received: December 2004; Revised: April 2005; Published: August 2005.
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