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

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-21 DOI:10.3390/axioms13060341

Sania Qureshi, F. Chicharro, Ioannis K. Argyros, Amanullah Soomro, Jihan Alahmadi, E. Hıncal

引用次数: 0

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.

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利用局部、半局部和稳定性分析求解非线性方程系统的新型最优数值根求解器

本文介绍了一种精度极高的迭代法，即四阶收敛法。该方法通过线性组合专门满足 Kung-Traub 猜想下的最优条件。该方法的效率指数约为 1.5874，采用了局部分析和半局部分析相结合的方法来提高效率和收敛性。本研究旨在研究半局部收敛性、动态分析以评估稳定性和收敛速度，以及所提求解器在非线性方程系统中的应用。研究结果凸显了所提方法在多义性和其他数学研究领域的应用潜力。所提出的优化方法的性能改进通过物理、机械、化学和燃烧等多个领域的数学模型得到了证明。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.