A new fifth-order iterative method free from second derivative for solving nonlinear equations

2021 ◽  
Author(s):  
Noori Yasir Abdul-Hassan ◽  
Ali Hasan Ali ◽  
Choonkil Park
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Second Derivative ◽  
Fifth Order

Fifth-order iterative method for finding multiple roots of nonlinear equations

2010 ◽  
Vol 57 (3) ◽  
pp. 389-398 ◽  
Author(s):  
Xiaowu Li ◽  
Chunlai Mu ◽  
Jinwen Ma ◽  
Linke Hou
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Multiple Roots ◽  
Fifth Order

scholarly journals A New Three Step Iterative Method without Second Derivative for Solving Nonlinear Equations

2015 ◽  
Vol 12 (3) ◽  
pp. 632-637 ◽  
Author(s):  
Baghdad Science Journal
Keyword(s):  
Finite Difference Method ◽  
Iterative Method ◽  
Nonlinear Equations ◽  
Linear Interpolation ◽  
New Method ◽  
Second Derivative ◽  
Third Order ◽  
Numerical Examples ◽  
Newton Equation ◽  
Interpolation Analysis

In this paper , an efficient new procedure is proposed to modify third –order iterative method obtained by Rostom and Fuad [Saeed. R. K. and Khthr. F.W. New third –order iterative method for solving nonlinear equations. J. Appl. Sci .7(2011): 916-921] , using three steps based on Newton equation , finite difference method and linear interpolation. Analysis of convergence is given to show the efficiency and the performance of the new method for solving nonlinear equations. The efficiency of the new method is demonstrated by numerical examples.

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.

Three novel fifth-order iterative schemes for solving nonlinear equations

2021 ◽  
Vol 187 ◽  
pp. 282-293
Author(s):  
Chein-Shan Liu ◽  
Essam R. El-Zahar ◽  
Chih-Wen Chang
Keyword(s):  
Nonlinear Equations ◽  
Iterative Schemes ◽  
Fifth Order
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