scholarly journals A NEW ONE PARAMETER FAMILY OF ITERATIVE METHODS WITH EIGHTH-ORDER OF CONVERGENCE FOR SOLVING NONLINEAR EQUATIONS

2013 ◽  
Vol 84 (5) ◽  
Author(s):  
H.I. Siyyam ◽  
M.T. Shatnawi ◽  
I.A. Al-Subaihi
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
Parameter Family ◽  
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.

scholarly journals Solving Nondifferentiable Nonlinear Equations by New Steffensen-Type Iterative Methods with Memory

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
J. P. Jaiswal
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
Efficiency Index ◽  
The Self ◽  
Function Evaluation ◽  
Eighth Order ◽  
Derivative Free ◽  
With Memory

It is attempted to present two derivative-free Steffensen-type methods with memory for solving nonlinear equations. By making use of a suitable self-accelerator parameter in the existing optimal fourth- and eighth-order without memory methods, the order of convergence has been increased without any extra function evaluation. Therefore, its efficiency index is also increased, which is the main contribution of this paper. The self-accelerator parameters are estimated using Newton’s interpolation. To show applicability of the proposed methods, some numerical illustrations are presented.

scholarly journals An Efficient Family of Optimal Eighth-Order Iterative Methods for Solving Nonlinear Equations and Its Dynamics

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Anuradha Singh ◽  
J. P. Jaiswal
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
Basins Of Attraction ◽  
Order Method ◽  
Eighth Order ◽  
New Family ◽  
Seventh Order ◽  
Prime Objective ◽  
And Performance

The prime objective of this paper is to design a new family of optimal eighth-order iterative methods by accelerating the order of convergence of the existing seventh-order method without using more evaluations for finding simple root of nonlinear equations. Numerical comparisons have been carried out to demonstrate the efficiency and performance of the proposed method. Finally, we have compared new method with some existing eighth-order methods by basins of attraction and observed that the proposed scheme is more efficient.

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 A Family of Fourteenth-Order Convergent Iterative Methods for Solving Nonlinear Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Fiza Zafar ◽  
Gulshan Bibi
Keyword(s):  
Iterative Method ◽  
Iterative Methods ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
Efficiency Index ◽  
Numerical Examples ◽  
New Class ◽  
First Derivative ◽  
New Methods ◽  
Specific Step

We present a family of fourteenth-order convergent iterative methods for solving nonlinear equations involving a specific step which when combined with any two-step iterative method raises the convergence order by n+10, if n is the order of convergence of the two-step iterative method. This new class include four evaluations of function and one evaluation of the first derivative per iteration. Therefore, the efficiency index of this family is 141/5 =1.695218203. Several numerical examples are given to show that the new methods of this family are comparable with the existing methods.

scholarly journals A New Biparametric Family of Two-Point Optimal Fourth-Order Multiple-Root Finders

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Young Ik Kim ◽  
Young Hee Geum
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Fourth Order ◽  
Order Of Convergence ◽  
Multiple Root ◽  
Multiple Roots ◽  
Asymptotic Error ◽  
Error Constant ◽  
Asymptotic Error Constant

We construct a biparametric family of fourth-order iterative methods to compute multiple roots of nonlinear equations. This method is verified to be optimally convergent. Various nonlinear equations confirm our proposed method with order of convergence of four and show that the computed asymptotic error constant agrees with the theoretical one.

scholarly journals Two Higher Order Iterative Methods for Solving Nonlinear Equations

2018 ◽  
Vol 14 (1) ◽  
pp. 179-187
Author(s):  
Jivandhar Jnawali ◽  
Chet Raj Bhatta
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
Higher Order ◽  
Secant Method ◽  
Subject Classification ◽  
Numerical Examples ◽  
Ams Subject Classification

 The main purpose of this paper is to derive two higher order iterative methods for solving nonlinear equations as variants of Mir, Ayub and Rafiq method. These methods are free from higher order derivatives. We obtain these methods by amalgamating Mir, Ayub and Rafiq method with standard secant method and modified secant method given by Amat and Busquier. The order of convergence of new variants are four and six. Also, numerical examples are given to compare the performance of newly introduced methods with the similar existing methods. 2010 AMS Subject Classification: 65H05 Journal of the Institute of Engineering, 2018, 14(1): 179-187

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
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