Dynamical Comparison of Several Third-Order Iterative Methods for Nonlinear Equations

作     者：Obadah Said Solaiman Samsul Ariffin Abdul Karim Ishak Hashim 

作者机构：Department of Mathematical SciencesFaculty of Science&TechnologyUniversiti Kebangsaan MalaysiaBangi Selangor43600Malaysia Department of Fundamental and Applied SciencesCenter for Smart Grid Energy Research(CSMER)Institute of Autonomous SystemUniversiti Teknologi PETRONASBandar Seri IskandarSeri IskandarPerak DR32610Malaysia 

出 版 物：《Computers, Materials & Continua》 (计算机、材料和连续体（英文）)

年 卷 期：2021年第67卷第5期

页      面：1951-1962页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：We are grateful for the financial support from UKM’s research Grant GUP-2019-033 

主　　题：Nonlinear equations iterative methods basins of attraction order of convergence 

摘      要：There are several ways that can be used to classify or compare iterative methods for nonlinear equations,for instance;order of convergence,informational efficiency,and efficiency *** this work,we use another way,namely the basins of attraction of the *** purpose of this study is to compare several iterative schemes for nonlinear *** the selected schemes are of the third-order of convergence and most of them have the same efficiency *** comparison depends on the basins of attraction of the iterative techniques when applied on several polynomials of different *** a comparison,we determine the CPU time(in seconds)needed by each scheme to obtain the basins of attraction,besides,we illustrate the area of convergence of these schemes by finding the number of convergent and divergent points in a selected range for all *** confirm the fact that basins of attraction differ for iterative methods of different orders,furthermore,they vary for iterative methods of the same order even if they have the same efficiency ***,this leads to the need for a new index that reflects the real efficiency of the iterative scheme instead of the commonly used efficiency index.