Numerical algorithm for nonlinear delayed differential systems of nth order

Abstract

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 three types of delays are considered. The accuracy of the results is compared to those obtained by the Laplace decomposition algorithm, the residual power series method and Matlab package DDENSD. A comparison of computing time is presented, too, showing reliability and efficiency of the proposed technique.