A Higher Order Chebyshev-Halley-Type Family of Iterative Methods for Multiple Roots

Ramandeep Behl, Eulalia Martínez, Fabricio Cevallos and Diego Alarcón
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Ramandeep Behl: Department of Mathematics, King Abdualziz University, Jeddah 21589, Saudi Arabia
Eulalia Martínez: Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain
Fabricio Cevallos: Fac. de Ciencias Económicas, Universidad Laica “Eloy Alfaro de Manabí”, Manabí 130214, Ecuador
Diego Alarcón: Departamento de Matemática Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain

Mathematics, 2019, vol. 7, issue 4, 1-12

Abstract: The aim of this paper is to introduce new high order iterative methods for multiple roots of the nonlinear scalar equation; this is a demanding task in the area of computational mathematics and numerical analysis. Specifically, we present a new Chebyshev–Halley-type iteration function having at least sixth-order convergence and eighth-order convergence for a particular value in the case of multiple roots. With regard to computational cost, each member of our scheme needs four functional evaluations each step. Therefore, the maximum efficiency index of our scheme is 1.6818 for α = 2 , which corresponds to an optimal method in the sense of Kung and Traub’s conjecture. We obtain the theoretical convergence order by using Taylor developments. Finally, we consider some real-life situations for establishing some numerical experiments to corroborate the theoretical results.

Keywords: nonlinear equations; multiple roots; Chebyshev–Halley-type; optimal iterative methods; efficiency index (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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