Differential Equations with State-Dependent Delays

Eberhard P. Hofer, Bernd Tibken and Frank Lehn
Additional contact information
Eberhard P. Hofer: Universität Ulm, Abteilung Meß-, Regel- und Mikrotechnik
Bernd Tibken: Universität—Gesamthochschule Wuppertal, Fachgruppe für Automatisierungstechnik und Technische Kybernetik (atk) Bergische
Frank Lehn: Universität Ulm, Abteilung Meß-, Regel- und Mikrotechnik

A chapter in Online Optimization of Large Scale Systems, 2001, pp 413-432 from Springer

Abstract: Abstract In this article an introduction to the wide field of retarded or delay differential equations with state-dependent delays is given. Hereby, the most important features of this type of differential equations which are profoundly different from ordinary differential equations are discussed. The presence of discontinuities in higher derivatives of the solution of delay differential equations require suitable integration methods. Thus, an efficient numerical code for the integration of delay differential equations is presented. This code is based on a fourth order RK one step algorithm. Furthermore, the presence of discontinuities may lead to severe problems when parameters are to be estimated using higher order optimization techniques. These problems are pointed out and a systematic way for the analysis of the smoothness of a least squares objective function is presented.

Keywords: Weak Coupling; Initial Function; Delay Differential Equation; Jump Discontinuity; Jump Point (search for similar items in EconPapers)
Date: 2001
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-04331-8_22

Ordering information: This item can be ordered from
http://www.springer.com/9783662043318

DOI: 10.1007/978-3-662-04331-8_22

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().