• Home
  1. Home
  2. Computing breaking points in implicit delay differential equations
Scientific article
OA Policy
English

Computing breaking points in implicit delay differential equations

Contributors

Guglielmi, Nicola; Hairer, Ernst

Published in

Advances in computational mathematics, vol. 29, no. 3, p. 229-247

Publication date

2008

Abstract

Systems of implicit delay differential equations, including state-dependent problems neutral and differential-algebraic equations, singularly perturbed problems, and small or vanishing delays are considered. The numerical integration of such problems is very sensitive to jump discontinuities in the solution or in its derivatives (so-called breaking points). In this article we discuss a new strategy - peculiar to implicit schemes - that allows codes to detect automatically and then to compute very accurately those breaking points which have to be inserted into the mesh to guarantee the required accuracy. In particular for state-dependent delays, where breaking points are not known in advance, this treatment leads to a significant improvement in accuracy. As a theoretical result we obtain a general convergence theorem which was missing in the literature (see cite{BZ03}). Furthermore, as a useful by-product, we design strategies that are able to detect points of non-uniqueness or non-existence of the solution so that the code can terminate when such a situation occurs. A new version of the code RADAR5 together with drivers for some real-life problems is available on the homepages of the authors.

Keywords

  • Implicit delay differential equations
  • Runge--Kutta methods
  • Radau IIA methods
  • Breaking points
  • Non-existence and non-uniqueness of solutions
  • Error control
  • Numerical well-posedness

UNIGE affiliation entities

Citation (ISO format)

GUGLIELMI, Nicola, HAIRER, Ernst. Computing breaking points in implicit delay differential equations. In: Advances in computational mathematics, 2008, vol. 29, n° 3, p. 229–247. doi: 10.1007/s10444-007-9044-5

Main files (1)

Article (Accepted version)

Identifiers

Additional URL for this publication

http://www.springerlink.com/content/62g810t42m1n1165/

Journal ISSN

1019-7168
691views
781downloads

Technical informations

Creation

16/02/2010 11:53:00

First validation

16/02/2010 11:53:00

Update

14/03/2023 15:24:06

Status update

14/03/2023 15:24:06

Last indexation

29/10/2024 13:00:42
All rights reserved by Archive ouverte UNIGE and the University of Geneva
OpenAIRE Indexed & Validated