Approximation of Linear Differential Equations with variable delay on an Infinite Interval

2016/07/23 by Sepúlveda, Daniel
#34K06 #34K07 #34K20 #34K28 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1607.06960

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 \citecooke1994.

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