Discontinuous solutions of neutral delay differential equations

Baker, C. T. H. and Paul, C. A. H. (2006) Discontinuous solutions of neutral delay differential equations. Applied Numerical Mathematics, 56 (3-4). pp. 284-304. ISSN 0168-9274

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It is well known that the solutions of delay differential and implicit and explicit neutral delay differential equations (NDDEs) may have discontinuous derivatives, but it has not been appreciated (sufficiently) that the solutions of NDDEs—and, therefore, solutions of delay differential algebraic equations—need not be continuous. Numerical codes for solving differential equations, with or without retarded arguments, are generally based on the assumption that a solution is continuous. We illustrate and explain how the discontinuities arise, and present some methods to deal with these problems computationally. The investigation of a simple example is followed by a discussion of more general NDDEs and further mathematical detail.

Item Type: Article
Uncontrolled Keywords: Neutral delay differential equations; Piecewise continuous solutions; Discontinuity tracking; Perturbed initial conditions; Delay differential algebraic equations; Singularly perturbed equations
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Ms Lucy van Russelt
Date Deposited: 22 Aug 2006
Last Modified: 20 Oct 2017 14:12
URI: https://eprints.maths.manchester.ac.uk/id/eprint/579

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