Work

Efficient Newton-Type Solvers Based on for Finding the Solution of Nonlinear Algebraic Problems

Year: 2024

Type: article

Abstract: The purpose of this study is to improve the computational efficiency of solvers for nonlinear algebraic problems with simple roots. To this end, a multi-step solver based on Newton’s method is utilized. Divided difference operators are applied at two substeps in various forms to enhance the convergence speed and, consequently, the solver’s efficiency index. Attraction basins for the proposed solvers and their competitors are presented, demonstrating that the proposed solvers exhibit large attraction basins in the scalar case while maintaining high convergence rates. Theoretical findings are supported by numerical experiments.

Source: Axioms

DOI: 10.3390/axioms13120880

Authors: Haifa Bin Jebreen, Hongzhou Wang, Yurilev Chalco-Cano

Institutions: King Saud University, Beijing Institute of Technology, University of Tarapacá

Language: English

Topic: Iterative Methods for Nonlinear Equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,728

Funder: King Saud University