The purpose of this paper is to propose a semi-analytical technique convenient for numerical approximation of solutions of the initial value problem for p-dimensional delayed and neutral differential systems with constant, proportional and time varying delays. The algorithm is based on combination of the method of steps and the differential transformation. Convergence analysis of the presented method is given as well. Applicability of the presented approach is demonstrated in two examples: A system of pantograph type differential equations and a system of neutral functional differential equations with all three types of delays considered. Accuracy of the results is compared to results obtained by the Laplace decomposition algorithm, the residual power series method and Matlab package DDENSD. Comparison of computing time is done too, showing reliability and efficiency of the proposed technique.

Abstract. In this article stability and asymptotic properties of a real two-dimensional system x ′ (t) = A(t)x(t) + n j=1 B j (t)x(t − r j ) + h(t, x(t), x(t − r 1 ), . . . , x(t − r n )) are studied, where r 1 > 0, . . . , r n > 0 are constant delays, A, B 1 , . . . , B n are the matrix functions and h is the vector function. Generalization of results on stability of a twodimensional differential system with one constant delay is obtained using the methods of complexification and Lyapunov-Krasovskii functional and some new corollaries and an example are presented. IntroductionThe investigation of the problem is based on the combination of the method of complexification and the method of Lyapunov-Krasovskii functional, which is to a great extent effective for two-dimensional systems. This combination was successfully used in [2] for two-dimensional system of ODE's and in [1] for system with one constant delay and led to interesting results.This article is related to paper [3] where asymptotic properties of system with finite number of constant delays were studied. The aim is, under some special conditions, to improve the results presented in [3] and to illustrate the advancement with an example.The subject of our study is the real two-dimensional systemwhere A(t) = a ik (t) , B j (t) = b jik (t) (i, k = 1, 2) for j ∈ {1, . . . , n} are real square matrices and 1991 Mathematics Subject Classification: 34K20, 34K25, 34K12.

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