Efficient computation of characteristic roots of delay differential equations using LMS methods
- 作者：Koen Verheyden ; Tatyana Luzyanina ; Dirk Roose
- 关键词：Delay differential equations ; Stability analysis ; Characteristic roots
- 刊名：Journal of Computational and Applied Mathematics
- 出版年：2008
- 期刊代码：72_03770427
- 类别：cp
- 出版时间：15 April 2008
- 卷：214
- 期：1
- 页码：209-226
- 文件大小：583 K
摘要
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.