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

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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.
Original languageEnglish
Pages (from-to)283-299
JournalNew Trends in Mathematical Sciences
Issue number1
Publication statusPublished - 21 Feb 2016
Externally publishedYes


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