Solving Nonlinear Differential Equation Arising in Dynamical Systems by AGM

In this paper, two nonlinear differential equations that appear in two specific dynamics problems,have been analyzed and solved completely by a simple and innovative approach in analytical methods which we have named it Akbari–Ganji’s method (AGM). Based on comparisons which have been made between the gained solutions by AGM, numerical method (Runge–Kutte 4th), variational iteration method and energy balanced method, it is possible to indicate that AGM can be successfully applied for various differential equations.Vibrational equations and solving them by AGM will be introduced firstly, and afterwards the application of AGM will be shown in the specified problems. It is noteworthy that this method has some valuable advantages, for instance in this approach, it is not necessary to utilize dimensionless parameters in order to simplify equation. So there is no need to convert the variables to new ones that heightens the complexity of the problem. More over by utilizing AGM, the shortage of boundary condition(s) for solving differential equation will be terminated by using derivatives of main differential equation(s). The results prove that this method is very effective, simple, reliable and can be applied for many other nonlinear problems. © 2016, Springer India Pvt. Ltd.