Title: An improved optimal eighth-order iterative scheme with its dynamical behaviour

Authors: Neha Choubey; J.P. Jaiswal

Addresses: Department of Mathematics, Oriental Institute of Science and Technology, Bhopal, M.P., 462021, India ' Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal, M.P., 462051, India

Abstract: In this paper, we have designed an improvement of the very recently constructed sixth-order iterative method without memory by using the weight function technique. Our scheme is optimal because it reaches the highest possible order using four function evaluations. Ten nonlinear test functions have been taken into account to check the reliability of the proposed scheme. Finally, dynamics of the proposed methods with some existing methods, illustrated in the paper.

Keywords: nonlinear equations; simple root; efficiency index; convergence order; dynamical behaviour; iterative schemes; optimisation; eighth-order iterative scheme; nonlinear test functions.

DOI: 10.1504/IJCSM.2016.078685

International Journal of Computing Science and Mathematics, 2016 Vol.7 No.4, pp.361 - 370

Received: 12 Jul 2014
Accepted: 04 May 2015
Published online: 01 Sep 2016 *

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