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

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.