On approximation of the solutions of delay differential equations by using piecewise constant arguments

Abstract

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).EPCAare 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.