A New Family of Optimal Fourth-Order Iterative Methods for Solving Nonlinear Equations With Applications

Ali Zein and Chong Lin

Journal of Applied Mathematics, 2024, vol. 2024, 1-22

Abstract: A new family of fourth-order iterative methods for solving nonlinear equations is proposed using the weight function procedure. This family is optimal in the sense of the Kung–Traub conjecture, as it requires three function evaluations per iteration. Due to its flexible structure, the new family offers a variety of options, demonstrating that it includes several well-known and recent methods as special cases. In particular, three new specific methods are designed to achieve better results compared to existing methods within the same family. Various nonlinear functions and engineering problems are used to illustrate the performance of these new specific methods, comparing them with existing ones. Furthermore, the analysis of complex dynamics and basins of attraction shows that the newly proposed methods yield the best results, with wider sets of initial points that lead to convergence.

Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/jam/2024/9955247.pdf (application/pdf)
http://downloads.hindawi.com/journals/jam/2024/9955247.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:9955247

DOI: 10.1155/2024/9955247

Access Statistics for this article

More articles in Journal of Applied Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().