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Efficient computation of characteristic roots of delay differential equations using LMS methods. (English) Zbl 1135.65349
Summary: 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.

##### MSC:
 65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations 34K28 Numerical approximation of solutions of functional-differential equations (MSC2010) 65L07 Numerical investigation of stability of solutions to ordinary differential equations 34K20 Stability theory of functional-differential equations
##### Software:
DDE-BIFTOOL; RODAS
Full Text:
##### References:
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