Fourth-Order Derivative-Free Optimal Families of King’s and Ostrowski’s Methods

2015 ◽  
pp. 359-371 ◽  
Author(s):  
Ramandeep Behl ◽  
S. S. Motsa ◽  
Munish Kansal ◽  
V. Kanwar
Keyword(s):  
Fourth Order ◽  
Order Derivative ◽  
Derivative Free

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 Ball convergence for a two-step fourth order derivative-free method for nonlinear equations

2019 ◽  
Vol 46 (2) ◽  
pp. 253-263
Author(s):  
Ioannis K. Argyros ◽  
Ramandeep Behl ◽  
S. S. Motsa
Keyword(s):  
Nonlinear Equations ◽  
Fourth Order ◽  
Order Derivative ◽  
Derivative Free ◽  
Derivative Free Method ◽  
Ball Convergence

scholarly journals Derivative-Free King’s Scheme for Multiple Zeros of Nonlinear Functions

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1242
Author(s):  
Ramandeep Behl ◽  
Sonia Bhalla ◽  
Eulalia Martínez ◽  
Majed Aali Alsulami
Keyword(s):  
Iterative Methods ◽  
Fourth Order ◽  
Order Of Convergence ◽  
Real Life ◽  
Multiple Roots ◽  
Computational Results ◽  
Nonlinear Functions ◽  
First Order ◽  
Life Problems ◽  
Derivative Free

There is no doubt that the fourth-order King’s family is one of the important ones among its counterparts. However, it has two major problems: the first one is the calculation of the first-order derivative; secondly, it has a linear order of convergence in the case of multiple roots. In order to improve these complications, we suggested a new King’s family of iterative methods. The main features of our scheme are the optimal convergence order, being free from derivatives, and working for multiple roots (m≥2). In addition, we proposed a main theorem that illustrated the fourth order of convergence. It also satisfied the optimal Kung–Traub conjecture of iterative methods without memory. We compared our scheme with the latest iterative methods of the same order of convergence on several real-life problems. In accordance with the computational results, we concluded that our method showed superior behavior compared to the existing methods.

Fourth Order Derivative Spectrophotometric Determination of Lead with 1,10-Phenanthroline and Rose Bengal

1993 ◽  
Vol 26 (3) ◽  
pp. 523-539 ◽  
Author(s):  
D. Sreevalsan Nair ◽  
T. Prasada Rao ◽  
C. S. P. Iyer ◽  
A. D. Damodaran
Keyword(s):  
Spectrophotometric Determination ◽  
Fourth Order ◽  
Rose Bengal ◽  
Order Derivative

Constructing third-order derivative-free iterative methods

2011 ◽  
Vol 88 (7) ◽  
pp. 1509-1518 ◽  
Author(s):  
Sanjay Kumar Khattri ◽  
Torgrim Log
Keyword(s):  
Iterative Methods ◽  
Order Derivative ◽  
Third Order ◽  
Derivative Free
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