Efficient Three-Step Class of Eighth-Order Multiple Root Solvers and Their Dynamics

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 ei...

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Bibliographic Details
Published in:Symmetry (Basel) 2019-07, Vol.11 (7), p.837
Main Authors: Alharbey, R. A., Kansal, Munish, Behl, Ramandeep, Machado, J. A. Tenreiro
Format: Article
Language:English
Subjects:
Algorithms
Convergence
Global positioning systems
GPS
multiple roots
Neighborhoods
Nonlinear equations
optimal iterative methods
order of convergence
scalar equations
Weighting functions
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Summary: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.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym11070837