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Development of Optimal Eighth Order Derivative-Free Methods for Multiple Roots of Nonlinear Equations
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Efficient Three-Step Class of Eighth-Order Multiple Root Solvers and Their Dynamics

1
Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
2
School of Mathematics, Thapar Institute of Engineering and Technology, Patiala 147004, India
3
ISEP-Institute of Engineering, Polytechnic of Porto Department of Electrical Engineering, 431, 4294-015 Porto, Portugal
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(7), 837; https://doi.org/10.3390/sym11070837
Received: 27 May 2019 / Revised: 18 June 2019 / Accepted: 19 June 2019 / Published: 26 June 2019
(This article belongs to the Special Issue Symmetry with Operator Theory and Equations)
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Abstract

This article proposes a wide general class of optimal eighth-order techniques for approximating multiple zeros of scalar nonlinear equations. The new strategy adopts a weight function with an approach involving the function-to-function ratio. An extensive convergence analysis is performed for the eighth-order convergence of the algorithm. It is verified that some of the existing techniques are special cases of the new scheme. The algorithms are tested in several real-life problems to check their accuracy and applicability. The results of the dynamical study confirm that the new methods are more stable and accurate than the existing schemes. View Full-Text
Keywords: multiple roots; optimal iterative methods; scalar equations; order of convergence multiple roots; optimal iterative methods; scalar equations; order of convergence
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Alharbey, R.A.; Kansal, M.; Behl, R.; Machado, J.A.T. Efficient Three-Step Class of Eighth-Order Multiple Root Solvers and Their Dynamics. Symmetry 2019, 11, 837.

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