A convergent and stable fourth-order iterative procedure based on Kung-Traub conjecture for nonlinear systems

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-03-28 DOI:10.1016/j.apnum.2025.03.003

Asifa Tassaddiq , Sania Qureshi , Ioannis K. Argyros , Francisco I. Chicharro , Amanullah Soomro , Paras Nizamani , Evren Hincal

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引用次数: 0

Abstract

Iterative algorithms are essential in computer research because they solve nonlinear models. This study presents a new and efficient approach for finding the roots of nonlinear equations and nonlinear systems of equations. The algorithm follows a two-step process and aims to optimize the iterative process. Based on Kung-Traub conjecture, the method shows optimal convergence and only needs three function evaluations per iteration. This creates a fourth-order optimal iterative procedure with an efficiency index of about 1.5874. This method utilizes a combination of two well-established third-order iterative approaches. The analyses of local and semilocal convergence, as well as stability analysis using complex dynamics, provide substantial improvements compared to current methods. We have extensively tested the proposed algorithm on a range of nonlinear models, including chemical reactions, kinetic synthesis, and non-adiabatic stirred tank reactors, consistently demonstrating accurate and efficient results. In terms of both speed and accuracy, it outperforms contemporary algorithms.

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.