A comparison of perturbation techniques for nonlinear problems

H. A. Wahab
Department of Mathematics, Hazara University Mansehra, Pakistan.
Saira Bhatti
Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad, Pakistan.
Muhammad Naeem
Department of Information Technology, Hazara University Mansehra, Pakistan.

\(^{1}\)Corresponding Author: wahab@hu.edu.pk

Copyright © 2014 H. A. Wahab, Saira Bhatti, Muhammad Naeem. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: December, 2014.

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 perturbation method gives the same series solution as in Adomian Decomposition Method and we get the exact solution using two iterations only.

Keywords:

Perturbation Methods, Noise terms phenomena, Homotopy Perturbation Method, Adomian Decomposition Method.