Convergence and Stability of a Parametric Class of Iterative Schemes for Solving Nonlinear Systems

Alicia Cordero, Eva G. Villalba, Juan R. Torregrosa and Paula Triguero-Navarro
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Alicia Cordero: Multidisciplinary Institute of Mathematics, Universitat Politènica de València, 46022 València, Spain
Eva G. Villalba: Multidisciplinary Institute of Mathematics, Universitat Politènica de València, 46022 València, Spain
Juan R. Torregrosa: Multidisciplinary Institute of Mathematics, Universitat Politènica de València, 46022 València, Spain
Paula Triguero-Navarro: Multidisciplinary Institute of Mathematics, Universitat Politènica de València, 46022 València, Spain

Mathematics, 2021, vol. 9, issue 1, 1-18

Abstract: A new parametric class of iterative schemes for solving nonlinear systems is designed. The third- or fourth-order convergence, depending on the values of the parameter being proven. The analysis of the dynamical behavior of this class in the context of scalar nonlinear equations is presented. This study gives us important information about the stability and reliability of the members of the family. The numerical results obtained by applying different elements of the family for solving the Hammerstein integral equation and the Fisher’s equation confirm the theoretical results.

Keywords: nonlinear system; iterative method; divided difference operator; stability; parameter plane; dynamical plane (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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