Analyzing the nonlinear heat transfer equation by AGM

Abstract

In this paper, a novel nonlinear differential equation in the field of heat transfer has been investigated and solved completely by a new method that we called it Akbari-Ganjiâ Method (AGM). Regarding to the previously published papers, investigating this kind of equations is a very hard project to do and the obtained solution is not accurate and reliable. This issue will be appeared after comparing the obtained solution by Numerical Method or the Exact Solution. Based on the comparison which has been made between the achieved solutions by AGM and Numerical Method (Runge-Kutte 4th), it is possible to indicate that AGM can be successfully applied to various differential equations particularly for difficult ones. Furthermore, It is necessary to mention that a summary of the excellence of this method in comparison with other approaches can be considered as follows: Boundary conditions are required in accordance with order of the differential equation, this approach can create additional new boundary conditions in regard to the own differential equation and its derivatives. Therefore, it is logical to mention which AGM is operational for miscellaneous nonlinear differential equations in comparison with the other methods.

Keywords

• Akbari-Ganji’sMethod (AGM),nonlinear equation of heat transfer

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