Abstract
It is demonstrated that the method of steps for linear delay-differential equation together with the inverse Laplace transform can be used to find a converging sequence of polynomial approximants to the transcendental function determining stability of the delay equation. Numerical stability charts are shown to illustrate convergence. This approach can serve as a basis for an efficient numerical method to determine stability regions for higher-order delay-differential equations
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This paper is dedicated to the memory of professor Miklós Farkas, colleague and friend.
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Kalmár-Nagy, T. Stability analysis of delay-differential equations by the method of steps and inverse Laplace transform. Differ Equ Dyn Syst 17, 185–200 (2009). https://doi.org/10.1007/s12591-009-0014-x
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DOI: https://doi.org/10.1007/s12591-009-0014-x