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An algorithm to detect small solutions in linear delay differential equations. (English) Zbl 1092.65058

Summary: This paper presents an algorithm that provides a simple reliable mechanism for the detection of small solutions in linear delay differential equations. We provide background that emphasises the importance of detecting small solutions, we review existing experimental results and provide a mathematical justification for our choice of algorithm. The paper concludes with some examples.

MSC:

65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
34K06 Linear functional-differential equations
34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
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[8] N.J. Ford, P.M. Lumb, Detecting small solutions for delay differential equations with delay and period commensurate: a numerical approach, in preparation.; N.J. Ford, P.M. Lumb, Detecting small solutions for delay differential equations with delay and period commensurate: a numerical approach, in preparation.
[9] N.J. Ford, S.M. Verduyn Lunel, Numerical approximation of delay differential equations with small solutions, Proceedings of 16th IMACS World Congress on Scientific Computation, Applied Mathematics and Simulation, Lausanne 2000, paper 173-3, New Brunswick, 2000 (ISBN 3-9522075-1-9).; N.J. Ford, S.M. Verduyn Lunel, Numerical approximation of delay differential equations with small solutions, Proceedings of 16th IMACS World Congress on Scientific Computation, Applied Mathematics and Simulation, Lausanne 2000, paper 173-3, New Brunswick, 2000 (ISBN 3-9522075-1-9).
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