Scientific article

Geometric proofs of numerical stability for delay equations

Published inIMA journal of numerical analysis, vol. 21, no. 1, p. 439-450
Publication date2001

In this paper, asymptotic stability properties of implicit Runge Kutta methods for delay differential equations are considered with respect to the test equation $y'(t) = a y(t) + b y(t-1)$ with $a,b in C$. In particular, we prove that symmetric methods and all methods of even order cannot be unconditionally stable with respect to the considered test equation, while many of them are stable on problems where $a in R$ and $binC$. Furthermore, we prove that Radau IIA methods are stable on the subclass for equations where $a = alpha + i gamma$ with $alpha, gamma in R$, $gamma$ sufficiently small, and $bin C$.

  • Delay differential equations
  • Runge-Kutta methods
  • Asymptotic stability
  • Root locus technique
Citation (ISO format)
GUGLIELMI, Nicola, HAIRER, Ernst. Geometric proofs of numerical stability for delay equations. In: IMA journal of numerical analysis, 2001, vol. 21, n° 1, p. 439–450. doi: 10.1093/imanum/21.1.439
Main files (1)
Article (Published version)
ISSN of the journal0272-4979

Technical informations

Creation10/25/2010 11:07:00 AM
First validation10/25/2010 11:07:00 AM
Update time03/14/2023 4:08:22 PM
Status update03/14/2023 4:08:22 PM
Last indexation01/15/2024 9:46:53 PM
All rights reserved by Archive ouverte UNIGE and the University of GenevaunigeBlack