On Constructing a Family of Sixth-Order Methods for Multiple Roots

IF 3.6 2区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Fractal and Fractional Pub Date : 2023-12-11 DOI:10.3390/fractalfract7120878

Y. Geum

引用次数: 0

Abstract

A family of three-point, sixth-order, multiple-zero solvers is developed, and special cases of weight functions are investigated based on polynomials and low-order rational functions. The chosen cases of the proposed iterative method are compared with existing methods. The experiments show the superiority of the proposed schemes in terms of the number of divergent points and the average number of function evaluations per point. The dynamical characteristics of the developed methods, along with their illustrations, are represented with detailed analyses, comparisons, and comments.

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论构建多根六阶方法族

开发了一个三点、六阶、多零求解器系列，并研究了基于多项式和低阶有理函数的权重函数特例。所选的迭代法案例与现有方法进行了比较。实验结果表明，在分歧点数量和每个点的平均函数评估次数方面，所提出的方案更胜一筹。在详细分析、比较和评论的同时，还介绍了所开发方法的动态特性及其图解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Fractal and Fractional MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

4.60

自引率

18.50%

发文量

632

审稿时长

11 weeks

期刊介绍： Fractal and Fractional is an international, scientific, peer-reviewed, open access journal that focuses on the study of fractals and fractional calculus, as well as their applications across various fields of science and engineering. It is published monthly online by MDPI and offers a cutting-edge platform for research papers, reviews, and short notes in this specialized area. The journal, identified by ISSN 2504-3110, encourages scientists to submit their experimental and theoretical findings in great detail, with no limits on the length of manuscripts to ensure reproducibility. A key objective is to facilitate the publication of detailed research, including experimental procedures and calculations. "Fractal and Fractional" also stands out for its unique offerings: it warmly welcomes manuscripts related to research proposals and innovative ideas, and allows for the deposition of electronic files containing detailed calculations and experimental protocols as supplementary material.