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Advances in Mathematical Physics
Volume 2016 (2016), Article ID 7909632, 8 pages
http://dx.doi.org/10.1155/2016/7909632
Research Article

A Comparative Approach to the Solution of the Zabolotskaya-Khokhlov Equation by Iteration Methods

National College of Business Administration and Economics, Gulberg-III, 54660 Lahore, Pakistan

Received 9 October 2015; Revised 26 December 2015; Accepted 27 December 2015

Academic Editor: Soheil Salahshour

Copyright © 2016 Saeed Ahmed and Muhammad Kalim. 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.

Abstract

We employed different iteration methods like Homotopy Analysis Method (HAM), Adomian Decomposition Method (ADM), and Variational Iteration Method (VIM) to find the approximate solution to the Zabolotskaya-Khokhlov (ZK) equation. Iteration methods are used to solve linear and nonlinear PDEs whose classical methods are either very complex or too limited to apply. A comparison study has been made to see which of these methods converges to the approximate solution rapidly. The result revealed that, amongst these methods, ADM is more effective and simpler tool in its nature which does not require any transformation or linearization.