Solving Non-autonomous System of Nonlinear Ordinary Differential Equations Using Multi-stage Differential Transform Method
Differential equations are essential tools to model many problems in science, chemistry, physics, economics, and natures. There is no general technique to solve a non-autonomous system of nonlinear differential equations. Hence, in this paper, we propose solving a non-autonomous nonlinear system of several ordinary differential equations by using multistage differential transform method. The comparison between the numerical results that areobtained by multistage differential transform method and Runge-Kutta method are presented. The results show that multistage differential transform method (MsDTM) for many model problems gives a more accurate approximation than the Runge-Kutta numerical method for the solution of non-autonomous nonlinear ordinary differential systems. Furthermore, our technique solves non-autonomous nonlinear systems without linearization or restrictive assumptions.
Keywords - Multistage Differential Transform Method, Non-autonomous System, Nonlinear Ordinary Differential Equations, Differential Transform Method.