New fourth- and sixth-order classes of iterative methods for solving systems of nonlinear equations and their stability analysis

2020 ◽  
Author(s):  
Munish Kansal ◽  
Alicia Cordero ◽  
Sonia Bhalla ◽  
Juan R. Torregrosa
Keyword(s):  
Stability Analysis ◽  
Iterative Methods ◽  
Nonlinear Equations ◽  
Sixth Order ◽  
Systems Of Nonlinear Equations

scholarly journals Modified Potra-Pták Multi-step Schemes with Accelerated Order of Convergence for Solving Systems of Nonlinear Equations

2018 ◽  
Vol 24 (1) ◽  
pp. 3
Author(s):  
Himani Arora ◽  
Juan Torregrosa ◽  
Alicia Cordero
Keyword(s):  
Nonlinear Equations ◽  
Order Of Convergence ◽  
Sixth Order ◽  
Systems Of Nonlinear Equations ◽  
Order Method ◽  
Third Order ◽  
Boundary Problems ◽  
Newton Step ◽  
The Family ◽  
Efficiency And Reliability

In this study, an iterative scheme of sixth order of convergence for solving systems of nonlinear equations is presented. The scheme is composed of three steps, of which the first two steps are that of third order Potra-Pták method and last is weighted-Newton step. Furthermore, we generalize our work to derive a family of multi-step iterative methods with order of convergence 3 r + 6 , r = 0 , 1 , 2 , … . The sixth order method is the special case of this multi-step scheme for r = 0 . The family gives a four-step ninth order method for r = 1 . As much higher order methods are not used in practice, so we study sixth and ninth order methods in detail. Numerical examples are included to confirm theoretical results and to compare the methods with some existing ones. Different numerical tests, containing academical functions and systems resulting from the discretization of boundary problems, are introduced to show the efficiency and reliability of the proposed methods.

Efficient three-step iterative methods with sixth order convergence for nonlinear equations

2009 ◽  
Vol 53 (4) ◽  
pp. 485-495 ◽  
Author(s):  
Alicia Cordero ◽  
José L. Hueso ◽  
Eulalia Martínez ◽  
Juan R. Torregrosa
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Sixth Order ◽  
Order Convergence

SOME HIGH ORDER ITERATIVE METHODS FOR NONLINEAR EQUATIONS BASED ON THE MODIFIED HOMOTOPY PERTURBATION METHODS

2010 ◽  
Vol 03 (03) ◽  
pp. 395-408
Author(s):  
Bilian Chen ◽  
Yajun Xie ◽  
Changfeng Ma
Keyword(s):  
Nonlinear Equation ◽  
Iterative Methods ◽  
Nonlinear Equations ◽  
Perturbation Methods ◽  
Systems Of Nonlinear Equations ◽  
Convergence Criteria ◽  
Numerical Examples ◽  
Homotopy Perturbation ◽  
Nonlinear Equation Systems ◽  
High Order Iterative Methods

In this paper, we present some efficient iterative methods for solving nonlinear equation (systems of nonlinear equations, respectively) by using modified homotopy perturbation methods. We also discuss the convergence criteria of the present methods. Some numerical examples are given to illustrate the performance and efficiency of the proposed methods.

scholarly journals A Family of Iterative Methods for Solving Systems of Nonlinear Equations Having Unknown Multiplicity

Algorithms ◽  
2015 ◽  
Vol 9 (1) ◽  
pp. 5 ◽  
Author(s):  
Fayyaz Ahmad ◽  
S. Serra-Capizzano ◽  
Malik Ullah ◽  
A. Al-Fhaid
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Systems Of Nonlinear Equations

On Iterative Methods with Accelerated Convergence for Solving Systems of Nonlinear Equations

2011 ◽  
Vol 151 (1) ◽  
pp. 163-174 ◽  
Author(s):  
J. A. Ezquerro ◽  
M. Grau-Sánchez ◽  
A. Grau ◽  
M. A. Hernández ◽  
M. Noguera ◽  
...  
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Systems Of Nonlinear Equations ◽  
Accelerated Convergence
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