Stability of Certain Neutral Type Differential Equation and Numerical Experiment Via Differential Transform Method

Abstract

In this study, we obtain both the asymptotically stability and the numerical solution of first order neutral type differential equation with multiple retarded arguments. We first obtain sufficient specific conditions expressed in terms of linear matrix inequality (LMI) using the Lyapunov method to establish the asymptotic stability of solutions. Secondly, we use the differential transform method (DTM) to show numerical solutions. Finally, two examples are presented to demonstrate the effectiveness and applicability of proposed methods by Matlab and an appropriate computer program. © 2021, Bayram Sahin. All rights reserved.