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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 the Perov’s contraction principle and the step method. Also, we propose a new algorithm of successive approximation sequence generated by the step method and, as an example, we consider some second order delay differential equations with initial conditions.

AN EFFICIENT STEP METHOD FOR A SYSTEM OF DIFFERENTIAL EQUATIONS WITH DELAY