Second derivative free sixth order continuation method for solving nonlinear equations with applications

2018 ◽  
Vol 56 (7) ◽  
pp. 2099-2116 ◽  
Author(s):  
P. Maroju ◽  
Á. A. Magreñán ◽  
S. S. Motsa ◽  
Í. Sarría
Keyword(s):  
Nonlinear Equations ◽  
Continuation Method ◽  
Sixth Order ◽  
Second Derivative ◽  
Derivative Free

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.

scholarly journals Numerical Algorithms for Finding Zeros of Nonlinear Equations and Their Dynamical Aspects

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Amir Naseem ◽  
M. A. Rehman ◽  
Thabet Abdeljawad ◽  
Francisco Balibrea
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
Numerical Algorithms ◽  
One Dimension ◽  
Second Derivative ◽  
Numerical Examples ◽  
Derivative Free ◽  
Interpolation Technique ◽  
Taylor’S Series

In this paper, we developed two new numerical algorithms for finding zeros of nonlinear equations in one dimension and one of them is second derivative free which has been removed using the interpolation technique. We derive these algorithms with the help of Taylor’s series expansion and Golbabai and Javidi’s method. The convergence analysis of these algorithms is discussed. It is established that the newly developed algorithms have sixth order of convergence. Several numerical examples have been solved which prove the better efficiency of these algorithms as compared to other well-known iterative methods of the same kind. Finally, the comparison of polynomiographs generated by other well-known iterative methods with our developed algorithms has been made which reflects their dynamical aspects.

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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