Numerical Algorithm for Nonlinear Delayed Differential Systems of nnth Order

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.Comment: arXiv admin note: text overlap with arXiv:1501.00411 Author's reply: the text overlap may be caused by the fact that this article is concerning systems of equations, while the other paper was about single equation

Stability of a Functional Differential System with a Finite Number of Delays

The paper is devoted to the study of asymptotic properties of a real two-dimensional differential system with unbounded nonconstant delays. The sufficient conditions for the stability and asymptotic stability of solutions are given. Used methods are based on the transformation of the considered real system to one equation with complex-valued coefficients. Asymptotic properties are studied by means of Lyapunov-Krasovskii functional. The results generalize some previous ones, where the asymptotic properties for two-dimensional systems with one or more constant delays or one nonconstant delay were studied

On a solvable class of nonlinear difference equations of fourth order

We consider a class of nonlinear difference equations of the fourth order, which extends some equations in the literature. It is shown that the class of equations is solvable in closed form explaining theoretically, among other things, solvability of some previously considered very special cases. We also present some applications of the main theorem through two examples, which show that some results in the literature are not correct

On the critical case in oscillation for differential equations with a single delay and with several delays

New nonoscillation and oscillation criteria are derived for scalar delay differential equationṡ t ≥ t 0 , in the critical case including equations with several unbounded delays, without the usual assumption that the parameters a, h, a k , and h k of the equations are continuous functions. These conditions improve and extend some known oscillation results in the critical case for delay differential equations