An efficient step method for a system of differential equations with delay

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

System of delay differential equations; step method; Picard operators; generalized fibre contraction principle

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

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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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