Abstract
In this paper, the homotopy perturbation method (HPM) and Aboodh transform are employed to obtain analytical solution of the porous medium equation. The proposed method (ATHPM) is an elegant combination of the new integral transform “Aboodh Transform” and the homotopy perturbation method. The porous medium equations have importance in engineering and sciences and constitute a good model for many systems in various fields. The results tell us that the proposed method is more efficient and easier to handle when is compared with existing other methods in such partial differential equations.
Highlights
The heat equation is one of the three classical linear partial differential equations of second order that form the basis of any elementary introduction to the area of PDEs, and only recently has it come to be fairly well understood
Motivated and inspired by the on-going research inthese areas, we consider a new method, which is called Aboodh transform homotopy perturbation method (ATHPM) [1,2,3,4]. This method is suggested by combining the homotopy perturbation method and Aboodh transform
Hassan Sedeeg: The Solution of Porous Medium Equation by Aboodh Homotopy Perturbation Method differential equation can be considered as the follow:
Summary
The heat equation is one of the three classical linear partial differential equations of second order that form the basis of any elementary introduction to the area of PDEs, and only recently has it come to be fairly well understood. Many researchers mainly had paid attention to studying the solution of nonlinear partial differential equations by using various methods. Among these are the variational iteration method [Biazar and Ghazvini (2007)] [11], Adomian decomposition method [Wazwaz (2001) and Biazar et al (2007)], homotopy perturbation method [Mehdi Dehghan and JalilManafian (2008)], homotopy analysis method [Najeeb Alam Khan, Asmat Ara, Muhammad Afzal and Azam Khan (2010)], Elzaki Homotopy Perturbation Method [8,9,10], and Laplace decomposition algorithm [Majid Khan, Muhammad Asif Gondal and Yasir Khan (2011)]. Motivated and inspired by the on-going research inthese areas, we consider a new method, which is called Aboodh transform homotopy perturbation method (ATHPM) [1,2,3,4].
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