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• Delay differential equations with impulses. • Self-support condition. • Numerical approximation using equations with piecewise constant arguments. • Existence of periodic solutions. In this paper we consider a scalar linear delay equation with constant delay associated with an impulsive self-support condition. We define a numerical approximation scheme using a sequence of approximate delay equations with piecewise constant arguments, and we show its theoretical convergence. We present numerical examples to illustrate the applicability of the method, and we also observe existence of periodic solutions of the impulsive delay equation using numerical studies. [ABSTRACT FROM AUTHOR]