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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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Stability Analysis of DDEs

Stability Analysis of DDEs

Chapter:
(p.248) 9 Stability Analysis of DDEs
Source:
Numerical Methods for Delay Differential Equations
Author(s):

Alfredo Bellen

Marino Zennaro

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198506546.003.0009

This chapter provides some definitions and results on the contractivity, boundedness, and asymptotic stability of test equations chosen from suitable classes of DDEs and neutral DDEs, which are useful for deriving numerical methods that preserve the same properties. Two main possible approaches are reported. One approach (stability for all delays or delay independent stability) involves finding conditions on the right-hand-side function such that the problem is stable for all or some classes of delays, typically for all constant delays. The other approach (stability for fixed delay or delay dependent stability) involves finding weaker conditions such that the desired stability property is guaranteed for specific delay.

Keywords:   contractivity, boundedness, asymptotic stability, test equations, fixed delay, delay independent stability, delay dependent stability

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