Numerical periodic orbits of neutral delay differential equations

Pages: 1057 - 1067, Volume 13, Issue 4, November 2005

doi:10.3934/dcds.2005.13.1057       Abstract        Full Text (352.5K)       Related Articles

Nicola Guglielmi - Dipartimento di Matematica Pura e Applicata, Università de L'Aquila, I-67100 L'Aquila, Italy (email)
Christian Lubich - Mathematisches Institut, Universität Tübingen, D-72076 Tübingen, Germany (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.
Mathematics Subject Classification:  65L05

Received: December 2004;      Revised: April 2005;      Published: August 2005.