A family of derivative-free methods for solving nonlinear equations

2021 ◽  
Author(s):  
Sunil Kumar ◽  
Janak Raj Sharma
Keyword(s):  
Nonlinear Equations ◽  
Derivative Free ◽  
Derivative Free Methods

Optimal Derivative-Free Methods for Solving Nonlinear Equations

2011 ◽  
Author(s):  
Alicia Cordero ◽  
José L. Hueso ◽  
Eulalia Martínez ◽  
Juan R. Torregrosa ◽  
Theodore E. Simos ◽  
...  
Keyword(s):  
Nonlinear Equations ◽  
Derivative Free ◽  
Derivative Free Methods

scholarly journals Solving Nonsmooth Equations Using Derivative-Free Methods

2012 ◽  
Vol 3 ◽  
pp. 37-45
Author(s):  
M.S.M. Bahgat ◽  
M.A. Hafiz
Keyword(s):  
Error Analysis ◽  
Nonlinear Equations ◽  
Divided Differences ◽  
Nonsmooth Equations ◽  
Linear Combinations ◽  
Cubic Convergence ◽  
Numerical Examples ◽  
Derivative Free ◽  
Derivative Free Methods ◽  
The Given

In this paper, a family of derivative-free methods of cubic convergence for solving nonlinear equations is suggested. In the proposed methods, several linear combinations of divided differences are used in order to get a good estimation of the derivative of the given function at the different steps of the iteration. The efficiency indices of the members of this family are equal to 1.442. The convergence and error analysis are given. Also, numerical examples are used to show the performance of the presented methods and to compare with other derivative-free methods. And, were applied these methods on smooth and nonsmooth equations.

scholarly journals New Eighth-Order Derivative-Free Methods for Solving Nonlinear Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Rajinder Thukral
Keyword(s):  
Nonlinear Equations ◽  
Convergence Order ◽  
Order Derivative ◽  
Optimal Order ◽  
Eighth Order ◽  
Optimal Order Of Convergence ◽  
New Family ◽  
Derivative Free ◽  
Derivative Free Methods ◽  
Iteration Methods

A new family of eighth-order derivative-free methods for solving nonlinear equations is presented. It is proved that these methods have the convergence order of eight. These new methods are derivative-free and only use four evaluations of the function per iteration. In fact, we have obtained the optimal order of convergence which supports the Kung and Traub conjecture. Kung and Traub conjectured that the multipoint iteration methods, without memory based onnevaluations could achieve optimal convergence order of . Thus, we present new derivative-free methods which agree with Kung and Traub conjecture for . Numerical comparisons are made to demonstrate the performance of the methods presented.

Some efficient derivative free methods with memory for solving nonlinear equations

2012 ◽  
Vol 219 (2) ◽  
pp. 699-707 ◽  
Author(s):  
Janak Raj Sharma ◽  
Rangan K. Guha ◽  
Puneet Gupta
Keyword(s):  
Nonlinear Equations ◽  
Derivative Free ◽  
Derivative Free Methods ◽  
With Memory
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