An efficient twelfth-order iterative method for finding all the solutions of nonlinear equations

2013 ◽  
Vol 13 (3-4) ◽  
pp. 309-320
Author(s):  
F. Soleymani
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations

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.

An iterative method for the computation of the solutions of nonlinear equations

CALCOLO ◽  
1999 ◽  
Vol 36 (1) ◽  
pp. 17-34 ◽  
Author(s):  
Francesco Costabile ◽  
Maria Italia Gualtieri ◽  
Stefano Serra Capizzano
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations

A new third-order iterative method for scalar nonlinear equations

2014 ◽  
Vol 8 ◽  
pp. 2141-2150 ◽  
Author(s):  
Shin Min Kang ◽  
Waqas Nazeer ◽  
Arif Rafiq ◽  
Chahn Yong Jung
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Third Order

An iterative method with cubic convergence for nonlinear equations

2006 ◽  
Vol 183 (2) ◽  
pp. 1249-1255 ◽  
Author(s):  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor ◽  
Syed Tauseef Mohyud-Din ◽  
Asim Shabbir
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Cubic Convergence
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