scholarly journals A new general eighth-order family of iterative methods for solving nonlinear equations

2012 ◽  
Vol 25 (12) ◽  
pp. 2262-2266 ◽  
Author(s):  
Y. Khan ◽  
M. Fardi ◽  
K. Sayevand
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Eighth Order

scholarly journals On Some Iterative Methods with Memory and High Efficiency Index for Solving Nonlinear Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Tahereh Eftekhari
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
High Efficiency ◽  
Efficiency Index ◽  
Order Convergence ◽  
Eighth Order ◽  
Additional Function ◽  
Numerical Comparisons ◽  
With Memory

Based on iterative methods without memory of eighth-order convergence proposed by Thukral (2012), some iterative methods with memory and high efficiency index are presented. We show that the order of convergence is increased without any additional function evaluations. Numerical comparisons are made to show the performance of the presented methods.

Numerical solution of nonlinear equations by an optimal eighth-order class of iterative methods

2012 ◽  
Vol 59 (1) ◽  
pp. 159-171 ◽  
Author(s):  
Fazlollah Soleymani ◽  
S. Karimi Vanani ◽  
Hani I. Siyyam ◽  
I. A. Al-Subaihi
Keyword(s):  
Numerical Solution ◽  
Iterative Methods ◽  
Nonlinear Equations ◽  
Eighth Order

scholarly journals Stability study of eighth-order iterative methods for solving nonlinear equations

2016 ◽  
Vol 291 ◽  
pp. 348-357 ◽  
Author(s):  
Alicia Cordero ◽  
Alberto Magreñán ◽  
Carlos Quemada ◽  
Juan R. Torregrosa
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Stability Study ◽  
Eighth Order

scholarly journals On two new families of iterative methods for solving nonlinear equations with optimal order

2011 ◽  
Vol 5 (1) ◽  
pp. 93-109 ◽  
Author(s):  
M. Heydari ◽  
S.M. Hosseini ◽  
G.B. Loghmani
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Efficiency Index ◽  
Convergence Order ◽  
Optimal Order ◽  
Eighth Order ◽  
Optimal Convergence ◽  
Numerical Comparisons ◽  
First Derivative ◽  
The Third

In this paper, two new families of eighth-order iterative methods for solving nonlinear equations is presented. These methods are developed by combining a class of optimal two-point methods and a modified Newton?s method in the third step. Per iteration the presented methods require three evaluations of the function and one evaluation of its first derivative and therefore have the efficiency index equal to 1:682. Kung and Traub conjectured that a multipoint iteration without memory based on n evaluations could achieve optimal convergence order 2n?1. Thus the new families of eighth-order methods agrees with the conjecture of Kung-Traub for the case n = 4. Numerical comparisons are made with several other existing methods to show the performance of the presented methods.

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