Asymptotically ordinary linear Volterra difference equations with infinite delay

Áron Fehér, Lőrinc Márton and Mihály Pituk

Applied Mathematics and Computation, 2020, vol. 386, issue C

Abstract: A class of linear Volterra difference equations with infinite delay is considered. It is shown that if the coefficient matrices are sufficiently small, then the Volterra difference equation is asymptotically equivalent to a linear ordinary difference equation at infinity. The coefficient matrix of the ordinary difference equation is a solution of an associated matrix equation which can be obtained by successive approximations. The eigenvalues of the approximating matrices converge exponentially to the characteristic roots of the Volterra difference equation. As a corollary, an efficient new method is obtained for the computation of the characteristic roots with an explicit error estimate.

Keywords: Volterra difference equation; Infinite delay; Characteristic root; Approximation; Asymptotic behavior (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:386:y:2020:i:c:s0096300320304574

DOI: 10.1016/j.amc.2020.125499

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