Numerical Algorithm for Nonlinear Delayed Differential Systems of $n$th Order
For researchers working on numerical solutions of delay differential equations, this provides an incremental improvement in accuracy and efficiency over existing techniques.
The paper proposes a semi-analytical algorithm for solving nth-order nonlinear delayed differential systems by combining the method of steps with differential transformation. The method is shown to be more accurate and efficient than existing methods on two example systems, with comparisons to Laplace decomposition, residual power series, and Matlab's DDENSD.
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.