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Numerical Stability Test of Neutral Delay Differential Equations
Author
Source
Mathematical Problems in Engineering
Issue
Vol. 2008, Issue 2008 (31 Dec. 2008), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2008-04-14
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
The stability of a delay differential equation can be investigated on the basis of the root location of the characteristic function.
Though a number of stability criteria are available, they usually do not provide any information about the characteristic root with maximal real part, which is useful in justifying the stability and in understanding the system performances.
Because the characteristic function is a transcendental function that has an infinite number of roots with no closed form, the roots can be found out numerically only.
While some iterative methods work effectively in finding a root of a nonlinear equation for a properly chosen initial guess, they do not work in finding the rightmost root directly from the characteristic function.
On the basis of Lambert W function, this paper presents an effective iterative algorithm for the calculation of the rightmost roots of neutral delay differential equations so that the stability of the delay equations can be determined directly, illustrated with two examples.
American Psychological Association (APA)
Wang, Z. H.. 2008. Numerical Stability Test of Neutral Delay Differential Equations. Mathematical Problems in Engineering،Vol. 2008, no. 2008, pp.1-10.
https://search.emarefa.net/detail/BIM-491504
Modern Language Association (MLA)
Wang, Z. H.. Numerical Stability Test of Neutral Delay Differential Equations. Mathematical Problems in Engineering No. 2008 (2008), pp.1-10.
https://search.emarefa.net/detail/BIM-491504
American Medical Association (AMA)
Wang, Z. H.. Numerical Stability Test of Neutral Delay Differential Equations. Mathematical Problems in Engineering. 2008. Vol. 2008, no. 2008, pp.1-10.
https://search.emarefa.net/detail/BIM-491504
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-491504