eng
International Academy of Ecology and Environmental Sciences
Computational Ecology and Software
2220-721X
2016-6-1
6
2
41
54
2
article
The exact solutions of nonlinear problems by Homotopy Analysis Method (HAM)
Hafiz Abdul Wahab
1
2
Saira Bhatti
1
2
Mohammad Naeem
1
2
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
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.
http://www.iaees.org/publications/journals/ces/articles/2016-6(2)/exact-solutions-of-nonlinear-problems-by-Homotopy-Analysis-Method.pdf
homotopy analysis method
nonlinear problems
perturbation methods