Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximation of Linear Differential Equations with variable delay on an
  Infinite Interval   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}.

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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an