Another sixth-order iterative method free from derivative for solving multiple roots of a nonlinear equation

2017 ◽  
Vol 11 ◽  
pp. 2121-2129
Author(s):  
Rahma Qudsi ◽  
M. Imran ◽  
Syamsudhuha
Keyword(s):  
Nonlinear Equation ◽  
Iterative Method ◽  
Sixth Order ◽  
Multiple Roots

scholarly journals Fifth-Order Iterative Method for Solving Multiple Roots of the Highest Multiplicity of Nonlinear Equation

Algorithms ◽  
2015 ◽  
Vol 8 (3) ◽  
pp. 656-668 ◽  
Author(s):  
Juan Liang ◽  
Xiaowu Li ◽  
Zhinan Wu ◽  
Mingsheng Zhang ◽  
Lin Wang ◽  
...  
Keyword(s):  
Nonlinear Equation ◽  
Iterative Method ◽  
Multiple Roots ◽  
Fifth Order

scholarly journals A New Sixth-Order Steffensen-Type Iterative Method for Solving Nonlinear Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Tahereh Eftekhari
Keyword(s):  
Nonlinear Equation ◽  
Iterative Method ◽  
Nonlinear Equations ◽  
Efficiency Index ◽  
Sixth Order ◽  
New Method ◽  
Derivative Free ◽  
Better Than

Based on iterative method proposed by Basto et al. (2006), we present a new derivative-free iterative method for solving nonlinear equations. The aim of this paper is to develop a new method to find the approximation of the root α of the nonlinear equation f(x)=0. This method has the efficiency index which equals 61/4=1.5651. The benefit of this method is that this method does not need to calculate any derivative. Several examples illustrate that the efficiency of the new method is better than that of previous methods.

An Efficient Sixth-Order Convergent Newton-Type Iterative Method for Nonlinear Equations

2012 ◽  
Vol 220-223 ◽  
pp. 2585-2588
Author(s):  
Zhong Yong Hu ◽  
Fang Liang ◽  
Lian Zhong Li ◽  
Rui Chen
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Efficiency Index ◽  
Sixth Order ◽  
Type Method ◽  
Second Derivatives ◽  
Better Than

In this paper, we present a modified sixth order convergent Newton-type method for solving nonlinear equations. It is free from second derivatives, and requires three evaluations of the functions and two evaluations of derivatives per iteration. Hence the efficiency index of the presented method is 1.43097 which is better than that of classical Newton’s method 1.41421. Several results are given to illustrate the advantage and efficiency the algorithm.

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