Jump to ContentJump to Main Navigation
Numerical Methods for Delay Differential Equations$
Users without a subscription are not able to see the full content.

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

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2020. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 04 June 2020

Introduction

Introduction

Chapter:
(p.1) 1 Introduction
Source:
Numerical Methods for Delay Differential Equations
Author(s):

Alfredo Bellen

Marino Zennaro

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198506546.003.0001

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

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .