scholarly journals A fourth-order derivative-free algorithm for nonlinear equations

2011 ◽  
Vol 235 (8) ◽  
pp. 2551-2559 ◽  
Author(s):  
Yehui Peng ◽  
Heying Feng ◽  
Qiyong Li ◽  
Xiaoqing Zhang
Keyword(s):  
Nonlinear Equations ◽  
Fourth Order ◽  
Order Derivative ◽  
Derivative Free

scholarly journals A Newton Type Iterative Method with Fourth-order Convergence

2017 ◽  
Vol 12 (1) ◽  
pp. 87-95
Author(s):  
Jivandhar Jnawali
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Fourth Order ◽  
Newton's Method ◽  
Second Order ◽  
Secant Method ◽  
Order Derivative ◽  
Single Variable ◽  
Order Convergence ◽  
Numerical Examples

The aim of this paper is to propose a fourth-order Newton type iterative method for solving nonlinear equations in a single variable. We obtained this method by combining the iterations of contra harmonic Newton’s method with secant method. The proposed method is free from second order derivative. Some numerical examples are given to illustrate the performance and to show this method’s advantage over other compared methods.Journal of the Institute of Engineering, 2016, 12 (1): 87-95

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.

Sign in / Sign up

Export Citation Format

Share Document