Iterative Methods for Solving Seventh-Order Nonlinear Time Fractional Equations

2022 ◽  
Vol 8 (1) ◽  
pp. 147-175
Keyword(s):  
Iterative Methods ◽  
Fractional Equations ◽  
Seventh Order

scholarly journals Stability analysis of a parametric family of seventh-order iterative methods for solving nonlinear systems

2018 ◽  
Vol 323 ◽  
pp. 43-57 ◽  
Author(s):  
Abdolreza Amiri ◽  
Alicia Cordero ◽  
M. Taghi Darvishi ◽  
Juan R. Torregrosa
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Iterative Methods ◽  
Parametric Family ◽  
Seventh Order

scholarly journals A family of iterative methods with sixth and seventh order convergence for nonlinear equations

2010 ◽  
Vol 52 (9-10) ◽  
pp. 1490-1496 ◽  
Author(s):  
Alicia Cordero ◽  
José L. Hueso ◽  
Eulalia Martínez ◽  
Juan R. Torregrosa
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Order Convergence ◽  
Seventh Order

Local Convergence of a Family of Iterative Methods with Sixth and Seventh Order Convergence Under Weak Conditions

2019 ◽  
Vol 16 (08) ◽  
pp. 1850120 ◽  
Author(s):  
Tianbao liu ◽  
Xiwen Qin ◽  
Peng Wang
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Local Convergence ◽  
Basins Of Attraction ◽  
Order Convergence ◽  
The Family ◽  
Lipschitz Constants ◽  
Seventh Order ◽  
Parameter Values ◽  
Local Convergence Theorem

In this paper, we study a local convergence analysis of a family of iterative methods with sixth and seventh order convergence for nonlinear equations, which was established by [Cordero et al. [2010] in “A family of iterative methods with sixth and seventh order convergence for nonlinear equations,” Math. Comput. Model. 52, 1190–1496]. Earlier studies have shown convergence using Taylor expansions and hypotheses reaching up to the sixth derivative. In our work, we make an attempt to study and establish a local convergence theorem by using only hypotheses the first derivative of the function and Lipschitz constants. We can also obtain error bounds and radii of convergence based on our results. Hence, the applicability of the methods is expanded. Moreover, we consider some different numerical examples and obtain the radii of convergence centered at the solution for different parameter values [Formula: see text] of the family. Furthermore, the basins of attraction of the family with different parameter values are also studied, which allow us to distinguish between the good and bad members of the family in terms of convergence and stable properties, and help us find the members with better or the best stable behavior.

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.

Comparison of Direct and Iterative Methods for Model Updating of a Curved Cable-stayed Bridge Using Experimental Modal Data

2016 ◽  
Vol 106 (8) ◽  
pp. 538-545 ◽  
Author(s):  
Guanzhe Fa ◽  
Enrico Mazzarolo ◽  
Leqia He ◽  
Bruno Briseghella ◽  
Luigi Fenu ◽  
...  
Keyword(s):  
Iterative Methods ◽  
Model Updating ◽  
Modal Data ◽  
Cable Stayed Bridge
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