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 frac...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.展开更多
基金supported by the Anhui Provincial Natural Science Foundation(No.070416227)the Natural Science Foundation of Anhui Provincial Education Depart ment under Grant(No.KJ2008A027)
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)+1 种基金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)
文摘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.
