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Discrete Dynamics in Nature and Society
Volume 2017 (2017), Article ID 3794357, 8 pages
https://doi.org/10.1155/2017/3794357
Research Article

Decomposition Technique and a Family of Efficient Schemes for Nonlinear Equations

1Department of Mathematics, COMSATS Institute of Information Technology, Attock Campus, Attock, Pakistan
2School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia
3Department of Mathematics, University of Education, Attock Campus, Attock, Pakistan

Correspondence should be addressed to Farooq Ahmed Shah

Received 25 April 2017; Accepted 17 August 2017; Published 1 October 2017

Academic Editor: Qamar Din

Copyright © 2017 Farooq Ahmed Shah et al. 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

Various problems of pure and applied sciences can be studied in the unified framework of nonlinear equations. In this paper, a new family of iterative methods for solving nonlinear equations is developed by using a new decomposition technique. The convergence of the new methods is proven. For the implementation and performance of the new methods, some examples are solved and the results are compared with some existing methods.