Analyzing the nonlinear heat transfer equation by AGM

Abstract

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-Ganjis 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.

A Novel Hybrid Approach Leveraging Shehu Transformation, Akbari-Ganji’s Method, and Padé Approximant for the Resolution of Diffusive Prey-Predator Systems

“…This method, which was created by Mirgolbabaee et al [24], is a great one for computing and can be used to solve many nonlinear differential equations. It assumes that the answer is a finite series, so it must be obtained by solving a series of algebraic problems.…”

“…Among the many analytical methods for solving differential equations is the Akbari-Ganji approach, developed by Mirgolbabaee et al [24], applicable to a range of nonlinear ordinary and partial differential equations. Meanwhile, the Padé approximation, crafted by Henri Padé in 1890, optimizes the accuracy and convergence of solutions by approximating a function near a specific point [25].…”

Numerical Solution of Volterra Integro-Differential Equations by Akbari-Ganji’s Method

“…Using Perturbed Collocation Method (PCM) [12] solved Singular Multi-order Fractional Differential Equations (SMFDE) of Lane-Emden Type with results which converged to the exact solutions. Akbari-Ganji Method (AGM) was used by [13], [14], [15] and [16] to find the numerical solution of differential equations arising from different physical problems. The studies concluded that AGM is a strong method to solve linear, nonlinear and partial differential equations, especially vibrational, wave and heat transfer problems.…”