By using the Gronwall Bellman inequality we prove some limit relations
between the solutions of delay differential equations with continuous arguments and the
solutions of some related delay differential equations with piecewise constant
arguments(EPCA). EPCA are strongly related to some discrete difference equations
arising in numerical analysis, therefore the results can be used to compute numerical
solutions of delay differential equations. We also consider the delay differential
equations of neutral type by applying a generalization of the Gronwall Bellman
inequality.
