A Comparison Between Two Approaches to Solve Functional Differential Equations: DTM and DJM

Abstract

Differential Transform Method (DTM) is a Taylor series method for finding Adomian Polynomials along with the method of steps which is used to solve many linear and non-linear differential equations or systems of physical significance. Whereas, the Daftardar-Gejji andJafari Method (DJM) is a method developed by Varsha Daftardar-Gejji and H. Jafari [17] to solve non-linear Integral equations, Fractional differential equations, system of ODEs and so on. Montri Thongmoon and Sasitorn Pusjuso [13] have compared DTM and Laplace transform method to solve system of differential equations. Josef Rebenda et al. [2,10,11] have recently shown that DTM can be applied to functional differential equations with delay, whereas, Sachin Bhalekar and Jayvant Patade [16] have recently obtained solutions of system of delay differential equations with proportional delay using DJM in the form of a special function and studied it's properties. We compare these two iterative methods to solve differential equations. We further try to explore the possibility of these two numerical methods on delayed, hybrid dynamical and delayed hybrid models.