Efficient computation of characteristic roots of delay differential equations using LMS methods

Authors:
Koen Verheyden;Tatyana Luzyanina;Dirk Roose
Affiliations:
Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001 Heverlee-Leuven, Belgium;Institute of Mathematical Problems in Biology, RAS, Pushchino, Moscow region, 142290, Russian Federation;Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001 Heverlee-Leuven, Belgium
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

Citing 5
Cited 3

Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems

Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL

ACM Transactions on Mathematical Software (TOMS)
On Stability of LMS Methods and Characteristic Roots of Delay Differential Equations

SIAM Journal on Numerical Analysis
Pseudospectral Differencing Methods for Characteristic Roots of Delay Differential Equations

SIAM Journal on Scientific Computing
Solution operator approximations for characteristic roots of delay differential equations

Applied Numerical Mathematics - The third international conference on the numerical solutions of volterra and delay equations, May 2004, Tempe, AZ

Critical delays and polynomial eigenvalue problems

Journal of Computational and Applied Mathematics
A Krylov Method for the Delay Eigenvalue Problem

SIAM Journal on Scientific Computing
Reliably computing all characteristic roots of delay differential equations in a given right half plane using a spectral method

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	7.29

Visualization

Abstract

We aim at the efficient computation of the rightmost, stability-determining characteristic roots of a system of delay differential equations. The approach we use is based on the discretization of the time integration operator by a linear multistep (LMS) method. The size of the resulting algebraic eigenvalue problem is inversely proportional to the steplength. We summarize theoretical results on the location and numerical preservation of roots. Furthermore, we select nonstandard LMS methods, which are better suited for our purpose. We present a new procedure that aims at computing efficiently and accurately all roots in any right half-plane. The performance of the new procedure is demonstrated for small- and large-scale systems of delay differential equations.