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The purpose of this paper is to propose a semi-analytical techniqueconvenient for numerical approximation of solutions of the initial valueproblem for $p$-dimensional delayed and neutral differential systems withconstant, proportional and time varying delays. The algorithm is based oncombination of the method of steps and the differential transformation.Convergence analysis of the presented method is given as well. Applicability ofthe presented approach is demonstrated in two examples: A system of pantographtype differential equations and a system of neutral functional differentialequations with all three types of delays considered. Accuracy of the results iscompared to results obtained by the Laplace decomposition algorithm, theresidual power series method and Matlab package DDENSD. Comparison of computingtime is done too, showing reliability and efficiency of the proposed technique.

Numerical Algorithm for Nonlinear Delayed Differential Systems of $n$th Order