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Computational Ecology and Software, 2016, 6(2): 41-54
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Article

The exact solutions of nonlinear problems by Homotopy Analysis Method (HAM)

Hafiz Abdul Wahab1, Saira Bhatti2, Mohammad Naeem3
1Department of Mathematics, Hazara University, Manshera, Pakistan
2Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad, Pakistan
3Department of IT, Abbottabad University of Science and Technology, Abbottabad, Pakistan

Received 22 March 2016;Accepted 1 April 2016;Published online 1 June 2016
IAEES

Abstract
The present paper presents the comparison of analytical techniques. We establish the existence of the phenomena of the noise terms in the perturbation series solution and find the exact solution of the nonlinear problems. If the noise terms exist, the Homotopy Analysis method gives the same series solution as in Adomian Decomposition Method as well as homotopy Perturbation Method (Wahab et al, 2015) and we get the exact solution using the initial guess in Homotopy Analysis Method using the results obtained by Adomian Decomposition Method.

Keywords homotopy analysis method;nonlinear problems;perturbation methods.


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