Modification of Newton-Househölder Method for Determining Multiple Roots of Unknown Multiplicity of Nonlinear Equations

Syahmi Afandi Sariman, Ishak Hashim, Faieza Samat and Mohammed Alshbool
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Syahmi Afandi Sariman: Department of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, Bangi Selangor 43600, Malaysia
Ishak Hashim: Department of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, Bangi Selangor 43600, Malaysia
Faieza Samat: GENIUS@Pintar National Gifted Centre, Universiti Kebangsaan Malaysia, Bangi Selangor 43600, Malaysia
Mohammed Alshbool: Department of Applied Mathematics, Abu Dhabi University, Abu Dhabi, P.O. Box 59911, United Arab Emirates

Mathematics, 2021, vol. 9, issue 9, 1-12

Abstract: In this study, we propose an extension of the modified Newton-Househölder methods to find multiple roots with unknown multiplicity of nonlinear equations. With four functional evaluations per iteration, the proposed method achieves an optimal eighth order of convergence. The higher the convergence order, the quicker we get to the root with a high accuracy. The numerical examples have shown that this scheme can compete with the existing methods. This scheme is also stable across all of the functions tested based on the graphical basins of attraction.

Keywords: iteration method; multiple root; nonlinear equation; optimal convergence order (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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