Analytical Solving set of Nonlinear Differential Equationsin Engineering Fields and Basic Scienceby Enhanced AGM method

In this literature, set of complicated nonlinear differential equations in the field ofengineering have been analyzed and solved completely by algebraic method and we havenamed it enhanced Akbari-Ganji Method (AGME) As regards the previous publishedpapers, investigating this kind of equations is a very hard task to do and the obtainedsolution is not accurate and reliable. This issue will be emerged after comparing theachieved solutions by Numerical Method (Num.Rk ۴۵)or the Exact Solution. Based on thecomparisons which have been made between the gained solutions by AGM and NumericalMethod, it is possible to indicate that AGM can be successfully applied for variousdifferential equations particularly for difficult ones. Furthermore, It is necessary tomention that a summary of the excellence of this method in comparison with the otherapproaches can be considered as follows: Boundary conditions are needed in accordancewith the order of differential equations in the solution procedure but when the number ofboundary conditions is less than the order of the differential equation, this approach cancreate additional new boundary conditions in regard to the own differential equation andits derivatives. Therefore, it is logical to mention that AGM is operational for miscellaneousnonlinear differential equations in comparison with the other methods.

Keywords:

Enhanced Akbari- Ganji's Method (AGME) , Set of nonlinear differentialEquations , Analytical solution , New method , Modeling AGM method.