Performance of a New Sixth-Order Class of Iterative Schemes for Solving Non-Linear Systems of Equations

Marlon Moscoso-Martínez, Francisco I. Chicharro, Alicia Cordero () and Juan R. Torregrosa
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Marlon Moscoso-Martínez: Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, Camino de Vera s/n, 46022 València, Spain
Francisco I. Chicharro: Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, Camino de Vera s/n, 46022 València, Spain
Alicia Cordero: Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, Camino de Vera s/n, 46022 València, Spain
Juan R. Torregrosa: Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, Camino de Vera s/n, 46022 València, Spain

Mathematics, 2023, vol. 11, issue 6, 1-15

Abstract: This manuscript is focused on a new parametric class of multi-step iterative procedures to find the solutions of systems of nonlinear equations. Starting from Ostrowski’s scheme, the class is constructed by adding a Newton step with a Jacobian matrix taken from the previous step and employing a divided difference operator, resulting in a triparametric scheme with a convergence order of four. The convergence order of the family can be accelerated to six by setting two parameters, resulting in a uniparametric family. We performed dynamic and numerical development to analyze the stability of the sixth-order family. Previous studies for scalar functions allow us to isolate those elements of the family with stable performance for solving practical problems. In this regard, we present dynamical planes showing the complexity of the family. In addition, the numerical properties of the class are analyzed with several test problems.

Keywords: nonlinear systems of equations; multipoint iterative methods; analysis of convergence; real discrete dynamics; chaos and stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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