A New Optimal Numerical Root-Solver for Solving Systems of Nonlinear Equations Using Local, Semi-Local, and Stability Analysis-Reference-Cited by-同舟云学术

A New Optimal Numerical Root-Solver for Solving Systems of Nonlinear Equations Using Local, Semi-Local, and Stability Analysis

Published:2024-05-21 Issue:6 Volume:13 Page:341
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Qureshi Sania¹²^ORCID,Chicharro Francisco I.³^ORCID,Argyros Ioannis K.⁴^ORCID,Soomro Amanullah¹^ORCID,Alahmadi Jihan⁵^ORCID,Hincal Evren⁶^ORCID

Affiliation:

1. Department of Basic Sciences and Related Studies, Mehran University of Engineering & Technology, Jamshoro 76062, Pakistan

2. Department of Computer Science and Mathematics, Lebanese American University, Beirut P.O. Box 13-5053, Lebanon

3. Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, 46022 València, Spain

4. Department of Computing and Mathematics Sciences, Cameron University, Lawton, OK 73505, USA

5. Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia

6. Department of Mathematics, Near East University, 99138 Mersin, Turkey

Abstract

This paper introduces an iterative method with a remarkable level of accuracy, namely fourth-order convergence. The method is specifically tailored to meet the optimality condition under the Kung–Traub conjecture by linear combination. This method, with an efficiency index of approximately 1.5874, employs a blend of localized and semi-localized analysis to improve both efficiency and convergence. This study aims to investigate semi-local convergence, dynamical analysis to assess stability and convergence rate, and the use of the proposed solver for systems of nonlinear equations. The results underscore the potential of the proposed method for several applications in polynomiography and other areas of mathematical research. The improved performance of the proposed optimal method is demonstrated with mathematical models taken from many domains, such as physics, mechanics, chemistry, and combustion, to name a few.

Funder

Ayuda a Primeros Proyectos de Investigación (PAID-06-23), Vicerrectorado de Investigación de la Universitat Politècnica de València

Publisher

MDPI AG

Link

https://www.mdpi.com/2075-1680/13/6/341/pdf

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