An efficient twelfth-order iterative method for finding all the solutions of nonlinear equations

Article type: Research Article

Authors: Soleymani, F.

Affiliations: Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran. E-mail: fazlollah.soleymani@gmail.com

Abstract: In this study, the sixteenth-order iterative scheme of Li et al. [X. Li, C. Mu, J. Ma, C. Wang, Sixteenth-order method for nonlinear equations, Appl. Math. Com. 215 (2010), 3754–3758] is considered. We increase its efficiency index from 1.587 to 1.644, by reducing the number of evaluations from six to five per iteration. This goal is achieved by providing an approximation for the first-order derivative of the function in the fourth step. Error analysis will also be studied. In the sequel, some numerical instances are given to show the accuracy of the new obtained twelfth-order technique. Therein, another objective of this paper is achieved by proposing a hybrid method for finding all the real solutions of nonlinear equations.

Keywords: All the zeros, error equation, asymptotic error constant, hybrid method, iterative methods

DOI: 10.3233/JCM-2012-0447

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 13, no. 3-4, pp. 309-320, 2013