## Abstract

Using the step method, we study a system of delay differential equations and we prove the existence and uniqueness of the solution and the convergence of the successive approximation sequence using Perov’s contraction principle and the step method. Also, we propose a new algorithm of successive apprthe oximation sequence generated by the step method and, as an example, we consider some second order delay differential equations with initial conditions.

## Authors

D. **Otrocol**

(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy,

Technical University of Cluj-Napoca)

M.A. **Serban**

(Babes-Bolyai University)

## Keywords

## Cite this paper as:

D. Otrocol; M.A. Serban, *An efficient step method for a system of differential equations with delay*, J. Appl. Anal. Comput. Vol. 8 (2018) no. 2, pp. 498-508

## About this paper

##### Journal

Journal of Applied Analysis and Computation

##### Publisher Name

Wilmington Scientific Publisher, USA

##### Print ISSN

2156-907X

##### Online ISSN

2158-5644

##### MR

MR3760107

##### ZBL

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