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Exact solution for linear and nonlinear systems of PDEs by homotopy-perturbation method

Chowdhury, Md. Sazzad Hossien and Hashim, Ishak and Ismail, Ahmad Faris and Rahman, M. M. and Momani, Shaher Mohammad (2011) Exact solution for linear and nonlinear systems of PDEs by homotopy-perturbation method. Australian Journal of Basic and Applied Sciences, 5 (12). pp. 3295-3305. ISSN 1991-8178

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Abstract

In this paper, the homotopy-perturbation method (HPM)proposed by J.-H. He is adopted for solving linear and nonlinear systems of partial differential equations (PDEs). In this method, a homotopy parameter p, which takes the values from 0 to 1, is introduced. When p = 0, the system of equations usually reduces to a sufficiently simplified form, which normally admits a rather simple solution. As p gradually increases to 1, the system goes through a sequence of ‘deformations’, the solution of each of which is ‘close’ to that at the previous stage of ‘deformation’. Eventually at p = 1,the system takes the original form of the equation and the final stage of ‘deformation’ gives the desired solution. Some examples are presented to demonstrate the efficiency and simplicity of the method.

Item Type: Article (Journal)
Additional Information: 5807/19547
Uncontrolled Keywords: Exact solutions;Homotopy-perturbation method; System of PDEs
Subjects: Q Science > QA Mathematics > QA76 Computer software
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button): Kulliyyah of Engineering
Kulliyyah of Engineering > Department of Mechanical Engineering
Depositing User: Dr. Md Sazzad Hossien Chowdhury
Date Deposited: 17 Feb 2012 11:56
Last Modified: 17 Feb 2012 11:56
URI: http://irep.iium.edu.my/id/eprint/19547

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