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Open AccessArticle

Generating Root-Finder Iterative Methods of Second Order: Convergence and Stability

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Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, Avenida de La Paz 137, 26006 Logroño, Spain
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Multidisciplinary Mathematics Institute, Universitat Politècnica de València, Camino de Vera s/n, 46022 València, Spain
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Author to whom correspondence should be addressed.
Axioms 2019, 8(2), 55; https://doi.org/10.3390/axioms8020055
Received: 1 April 2019 / Revised: 30 April 2019 / Accepted: 30 April 2019 / Published: 6 May 2019
In this paper, a simple family of one-point iterative schemes for approximating the solutions of nonlinear equations, by using the procedure of weight functions, is derived. The convergence analysis is presented, showing the sufficient conditions for the weight function. Many known schemes are members of this family for particular choices of the weight function. The dynamical behavior of one of these choices is presented, analyzing the stability of the fixed points and the critical points of the rational function obtained when the iterative expression is applied on low degree polynomials. Several numerical tests are given to compare different elements of the proposed family on non-polynomial problems. View Full-Text
Keywords: nonlinear equations; iterative method; convergence; basin of attraction; stability nonlinear equations; iterative method; convergence; basin of attraction; stability
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Chicharro, F.I.; Cordero, A.; Garrido, N.; Torregrosa, J.R. Generating Root-Finder Iterative Methods of Second Order: Convergence and Stability. Axioms 2019, 8, 55.

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