A Fourth-Order Convergent Iterative Method by Means of Thiele's Continued Fraction for Root-Finding Problem  

作　　者：Shengfeng LI 

机构地区：[1]Institute of Applied Mathematics, Bengbu University

出　　处：《Journal of Mathematical Research with Applications》2019年第1期10-22,共13页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11571071);the Natural Science Key Foundation of Education Department of Anhui Province(Grant No.KJ2013A183);the Project of Leading Talent Introduction and Cultivation in Colleges and Universities of Education Department of Anhui Province(Grant No.gxfxZD2016270);the Incubation Project of the National Scientific Research Foundation of Bengbu University(Grant No.2018GJPY04)

摘　　要：In this paper, we propose a new single-step iterative method for solving non-linear equations in a variable. This iterative method is derived by using the approximation formula of truncated Thiele's continued fraction. Analysis of convergence shows that the order of convergence of the introduced iterative method for a simple root is four. To illustrate the efficiency and performance of the proposed method we give some numerical examples.In this paper, we propose a new single-step iterative method for solving non-linear equations in a variable. This iterative method is derived by using the approximation formula of truncated Thiele's continued fraction. Analysis of convergence shows that the order of convergence of the introduced iterative method for a simple root is four. To illustrate the efficiency and performance of the proposed method we give some numerical examples.

关 键 词：NON-LINEAR equation Thiele’s continued FRACTION Viscovatov algorithm iterative method order of convergence 

分 类 号：O1[理学—数学]