An assessment of a semi analytical AG method for solving nonlinear oscillators

In this paper, attempts have been made to solve nonlinear vibrational equation such as Van Der Pol Oscillator by utilizing a semi analytical Akbari-Ganji's Method (AGM). It is noticeable that there are some valuable advantages in this way of solving differential equations and also the answer of various sets of complicated differential equations can be achieved in this manner which in the other methods it would be difficult to obtain. Based on the comparison between AGM and numerical methods, AGM can be successfully applied for a broad range of nonlinear equations. One of the important reasons of selecting AGM for solving differential equations in miscellaneous fields not only in vibrations but also in different fields of sciences for instance fluid mechanics, solid mechanics, chemical engineering, etc. The main benefit of this method in comparison with the other approaches are as follows: normally according to the order of differential equations, we need boundary conditions so in the case of the number of boundary conditions is less than the order of the differential equation, AGM can create additional new boundary conditions in regard to the own differential equation and its derivatives. Results illustrate that method is efficient and has enough accuracy in comparison with other semi analytical and numerical methods because of the simplicity of this method. Moreover results demonstrate that AGM could be applicable through other methods in nonlinear problems with high nonlinearity. Furthermore convergence problems for solving nonlinear equations by using AGM appear small.