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.

Numerical periodic orbits of neutral delay differential equations

GUGLIELMI, NICOLA;
2005

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.
Neutral delay differential equations; periodic orbit; numerical solution; Runge-Kutta methods; Attractive invariant curves
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.12571/2810
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