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Numerical Methods for Delay Differential Equations$
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Alfredo Bellen and Marino Zennaro

Print publication date: 2003

Print ISBN-13: 9780198506546

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198506546.001.0001

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(p.1) 1 Introduction
Numerical Methods for Delay Differential Equations

Alfredo Bellen

Marino Zennaro

Oxford University Press

This chapter introduces the classes of DDEs and neutral DDEs treated in the book, focusing on some of the most significant qualitative differences between delay equations and ordinary equations, as well as on how such differences reflect in their numerical treatment. Some examples are given that stress the different behaviours of the solutions, either in terms of existence and uniqueness in dependence of the initial data, or in terms of the asymptotic behaviour in dependence of the parameters of the considered test problems. Evidence is given that integration of DDEs cannot be based on the mere adaptation of some standard ODE code to the presence of delayed terms. Integration of DDEs requires the use of specifically designed methods according to the nature of the equation and the behaviour of the solution.

Keywords:   delay equations, ordinary equations, DDEs, neutral DDEs, qualitative differences, numerical treatment, integration of DDEs

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