Exact versus discretized stability regions for a linear delay differential equation

Jan Čermák, Jiří Jánský and Luděk Nechvátal

Applied Mathematics and Computation, 2019, vol. 347, issue C, 712-722

Abstract: The paper introduces a system of necessary and sufficient stability conditions for a four-term linear delay difference equation with complex coefficients. These conditions are derived explicitly with respect to the time lag and can be viewed as a direct discrete counterpart to the existing stability results for the underlying delay differential equation. As a main proof tool, the boundary locus technique combined with some special results of the polynomial theory is employed. Since the studied difference equation serves as a θ-method discretization of its continuous pattern, several problems of numerical stability are discussed as well.

Keywords: Linear delay difference equation; Linear delay differential equation; θ-method discretization; Exact and numerical stability (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:347:y:2019:i:c:p:712-722

DOI: 10.1016/j.amc.2018.11.026

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