Approximation of Linear Differential Equations with variable delay on an Infinite Interval
Abstract
We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical approximation over an unbounded interval is in correspondence with the problem of transference of qualitative properties between a continuous and the corresponding discrete dynamical systems. We use theory of differential equations with delay and theory of integral inequality to prove our main result. We state sufficient conditions for: a) uniform approximation of solutions over an unbounded interval and b) transference of uniform asymptotic stability of non-autonomous linear differential equations with variable delay to the corresponding discrete difference equations. We improve and extended the results of \cite{cooke1994}.
Cite
@article{arxiv.1607.06960,
title = {Approximation of Linear Differential Equations with variable delay on an Infinite Interval},
author = {Daniel Sepúlveda},
journal= {arXiv preprint arXiv:1607.06960},
year = {2016}
}