Asymptotic behaviours of the solutions of neutral type Volterra integro-differential equations and some numerical solutions via differential transform method

Abstract

In this manuscript, we consider the first order neutral Volterra integro-differential equation (NVIDE) with delay argument. Firstly, we obtain novel sufficient conditions to establish the asymptotic behaviours of solutions of considered NVIDE using the Lyapunov method and present an example to demonstrate the applicability of proposed method. Secondly, we get some numerical solutions for a particular case of considered NVIDE via the differential transformation method (DTM). The results of this manuscript are novel and they improve some existing ones in the literature.

Keywords

• asymptotic behavior
• lyapunov functional
• nvide
• dtm