The exact solutions of nonlinear problems by Homotopy Analysis Method (HAM)
Hafiz Abdul Wahab
Saira Bhatti
Mohammad Naeem
Department of Mathematics, Hazara University, Manshera, Pakistan
Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad, Pakistan
Department of IT, Abbottabad University of Science and Technology, Abbottabad, Pakistan
Computational Ecology and Software
ISSN 2220-721X
http://www.iaees.org/publications/journals/ces/online-version.asp
2016
6
2
41
54
International Academy of Ecology and Environmental Sciences
Hong Kong
22 March 2016
1 April 2016
1 June 2016
homotopy analysis method
nonlinear problems
perturbation methods
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.
DOI 10.0000/issn-2220-721x-compuecol-2016-v6-0005
http://www.iaees.org/publications/journals/ces/articles/2016-6(2)/exact-solutions-of-nonlinear-problems-by-Homotopy-Analysis-Method.pdf