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, 2019. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 16 November 2019

Runge-Kutta Methods For DDEs

Runge-Kutta Methods For DDEs

Chapter:
(p.152) 6 Runge-Kutta Methods For DDEs
Source:
Numerical Methods for Delay Differential Equations
Author(s):

Alfredo Bellen

Marino Zennaro

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198506546.003.0006

This chapter specializes the standard approach presented in Chapter 4, based on the class of continuous Runge-Kutta methods reviewed in Chapter 5. The various cases of DDEs and neutral DDEs along the lines of Chapter 4 are reviewed, and further attention is given to the constant delay case for which the connection with Bellman's method of steps is illustrated. The non-vanishing, time-dependent delay case is investigated in detail, for which some additional results on superconvergence of constrained mesh methods are given, using the results on natural continuous extensions reported in Chapter 5. The numerical solution of the prototype of DDEs with vanishing delay, that is, the pantograph equation, is also investigated. RADAR5, the most recent code designed for a very general class of stiff delay differential-algebraic equations, is briefly introduced.

Keywords:   standard approach, Bellman's method, superconvergence, constrained mesh, constant delay, vanishing delay, pantograph equation

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 .