Numerical periodic orbits of neutral delay differential equations

Nicola Guglielmi; Christian Lubich

doi:10.3934/dcds.2005.13.1057

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2005, Volume 13, Issue 4: 1057-1067. Doi: 10.3934/dcds.2005.13.1057

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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
2.
Mathematisches Institut, Universität Tübingen, D-72076 Tübingen

Received: December 2004

Revised: April 2005

Published: July 2005

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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.

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Mathematics Subject Classification: 65L05.

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