Article

Homotopy analysis method for a nonlinear equation arising in heat transfer

Authors:
  • Islamic Azad University, Lashtenesha-Zibakenar Branch, Lashtenesha.Iran
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Abstract

An approximate analytic solution of a temperature distribution equation in a uniformly thick rectangular fin radiation to free space with nonlinearity of high order is formally obtained using the homotopy analysis method. It is shown that the freedom of choice of the auxiliary parameter k gives way to adjust and control the convergence of the solution series, which can be considered as a fundamental difference between the homotopy analysis method and other existing methods

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... HPM was proposed by Chinese mathematician He's in 1999 and successfully implemented to discover the several kinds of boundary value problems(He, 2006). The solution of RD equations by HPM presented byKumar et. ...
Article
Full-text available
In this article, we present a proficient semi-analytical method for solving the linear and nonlinear reaction-diffusion equations (RD equations) of Kolmogorov-Petrovsly-Piskunov equations (KPP equation) by new homotopy perturbation Method (NHPM). RD equations play a significant role in the arena of technology and sciences and then establish the best model for numerous organizations. The NHPM renovate a hard problem into a simple problem which can be simply cracked. Two numerical illustrations are given to check the capability and reliability of the proposed method. Obtained results from the proposed method (NHPM) are equated with the results of Homotopy perturbation method (HPM) and Adomian Decomposition Method (ADM). Software (MATLAB) is used to draw 3D graphs of the proposed method.
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