International Journal of Mathematics and Mathematical Sciences 
Volume 14 (1991), Issue 1, Pages 111-126
doi:10.1155/S016117129100011X

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

Istevan Györi1,2

 1Department of Mathematics, The University of Rhode Island, Kingston 02881, Rhode Island, USA
2Computing Centre of A. Szent-Györgyi Medical University, Pecsi u. 4/a., Szeged H - 6720, Hungary
Received 12 June 1989; Revised 30 June 1989

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). 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.