A general class of four parametric with- and without memory iterative methods for nonlinear equations

2019 ◽  
Vol 57 (5) ◽  
pp. 1448-1471
Author(s):  
Fiza Zafar ◽  
Alicia Cordero ◽  
Juan R. Torregrosa ◽  
Aneeqa Rafi
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
General Class

scholarly journals Novel Computational Iterative Methods with Optimal Order for Nonlinear Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
F. Soleymani
Keyword(s):  
Weight Function ◽  
Iterative Methods ◽  
Nonlinear Equations ◽  
Fourth Order ◽  
General Class ◽  
Analytical Study ◽  
Order Of Convergence ◽  
Optimal Order ◽  
Numerical Examples ◽  
First Order

This paper contributes a very general class of two-point iterative methods without memory for solving nonlinear equations. The class of methods is developed using weight function approach. Per iteration, each method of the class includes two evaluations of the function and one of its first-order derivative. The analytical study of the main theorem is presented in detail to show the fourth order of convergence. Furthermore, it is discussed that many of the existing fourth-order methods without memory are members from this developed class. Finally, numerical examples are taken into account to manifest the accuracy of the derived methods.

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 On the dynamics of a family of third-order iterative functions

2007 ◽  
Vol 48 (3) ◽  
pp. 343-359 ◽  
Author(s):  
Sergio Amat ◽  
Sonia Busquier ◽  
Sergio Plaza
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Conjugacy Classes ◽  
Complex Polynomials ◽  
Third Order ◽  
Iterative Functions

AbstractWe study the dynamics of a family of third-order iterative methods that are used to find roots of nonlinear equations applied to complex polynomials of degrees three and four. This family includes, as particular cases, the Chebyshev, the Halley and the super-Halleyroot-finding algorithms, as well as the so-called c-methods. The conjugacy classes of theseiterative methods are found explicitly.

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