Asymptotically ordinary linear Volterra difference equations with infinite delay
作者：
Highlights：
• A linear Volterra difference equation with infinite delay and sufficiently small coefficients is shown to be asymptotically equivalent to a linear ordinary difference equation.
• The coefficient matrix of the corresponding ordinary difference equation can be written as a limit of successive approximations.
• The eigenvalues of the approximating matrices converge to the characteristic roots of the Volterra difference equation at an exponential rate.
摘要
•A linear Volterra difference equation with infinite delay and sufficiently small coefficients is shown to be asymptotically equivalent to a linear ordinary difference equation.•The coefficient matrix of the corresponding ordinary difference equation can be written as a limit of successive approximations.•The eigenvalues of the approximating matrices converge to the characteristic roots of the Volterra difference equation at an exponential rate.
论文关键词：Volterra difference equation,Infinite delay,Characteristic root,Approximation,Asymptotic behavior
论文评审过程：Received 12 February 2020, Revised 30 April 2020, Accepted 28 June 2020, Available online 11 July 2020, Version of Record 11 July 2020.
论文官网地址：https://doi.org/10.1016/j.amc.2020.125499
