On numerical approximation using differential equations with piecewise-constant arguments

In this paper we give a brief overview of the application of delay differential equations with piecewise constant arguments (EPCAs) for obtaining numerical approximation of delay differential equations, and we show that this method can be used for numerical approximation in a class of age-dependent population models. We also formulate an open problem for a qualitative behaviour of a class of linear delay equations with continuous and piecewise constant arguments. AMS(MOS) subject classification: 34K28 keywords: delay equations; equations with piecewise constant arguments; numerical approximation, nonlinear age-dependent population model, hybrid equation.