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Journal of Mathematics
Volume 2016, Article ID 8174610, 7 pages
Research Article

Effective Root-Finding Methods for Nonlinear Equations Based on Multiplicative Calculi

1Faculty of Engineering, Cyprus International University, Nicosia, Mersin 10, Turkey
2Faculty of Education, Cyprus International University, Nicosia, Mersin 10, Turkey

Received 29 July 2016; Accepted 14 September 2016

Academic Editor: Liwei Zhang

Copyright © 2016 Ali Özyapıcı 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.


In recent studies, papers related to the multiplicative based numerical methods demonstrate applicability and efficiency of these methods. Numerical root-finding methods are essential for nonlinear equations and have a wide range of applications in science and engineering. Therefore, the idea of root-finding methods based on multiplicative and Volterra calculi is self-evident. Newton-Raphson, Halley, Broyden, and perturbed root-finding methods are used in numerical analysis for approximating the roots of nonlinear equations. In this paper, Newton-Raphson methods and consequently perturbed root-finding methods are developed in the frameworks of multiplicative and Volterra calculi. The efficiency of these proposed root-finding methods is exposed by examples, and the results are compared with some ordinary methods. One of the striking results of the proposed method is that the rate of convergence for many problems are considerably larger than the original methods.