Application to differential transformation method for solving systems of differential equations

In this paper, we present an analytical solution for different systems of differential equations by using the differential transformation method. The convergence of this method has been discussed with some examples which are presented to show the ability of the method for linear and non-linear systems of differential equations. We begin by showing how the differential transformation method applies to a non-linear system of differential equations and give two examples to illustrate the sufficiency of the method for linear and non-linear stiff systems of differential equations. The results obtained are in good agreement with the exact solution and Runge–Kutta method. These results show that the technique introduced here is accurate and easy to apply.