Work

Secant-Type Iterative Classes for Nonlinear Equations with Multiple Roots

Year: 2025

Type: article

Abstract: General-purpose iterative methods for solving nonlinear equations provide approximations to solving problems without closed-form solutions. However, these methods lose some properties when the problems have multiple roots or are not differentiable, in which case specific methods are used. However, in most problems the multiplicity of the root is unknown, which reduces the range of methods available to us. In this work we propose two iterative classes with memory for solving multiple-root nonlinear equations without knowing the multiplicity. One of the proposals includes derivatives, but the other is derivative-free, obtained from the previous one using divided differences and a parameter in its iterative expression. The order of convergence of the proposed schemes is analyzed. The stability of the methods is studied using real dynamics, showing the good behavior of the methods. A numerical benchmark confirms the theoretical study.

Source: Algorithms

DOI: 10.3390/a18090568

Authors: Francisco I. Chicharro, Neus Garrido-Saez, Julissa H. Jerezano

Institutions: Universitat Politècnica de València, National Autonomous University of Honduras

Language: English

Topic: Iterative Methods for Nonlinear Equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,930

Funder: Universitat Politècnica de València