scholarly journals An Efficient Two-step Iterative Method for Solving System of Nonlinear Equations

2012 ◽  
Vol 4 (4) ◽  
Author(s):  
MOHAMED SEBAK MOHAMED ◽  
M Ali Hafiz
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
System Of Nonlinear Equations

scholarly journals On a New Method for Computing the Numerical Solution of Systems of Nonlinear Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
H. Montazeri ◽  
F. Soleymani ◽  
S. Shateyi ◽  
S. S. Motsa
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
Efficiency Index ◽  
The Other ◽  
Systems Of Nonlinear Equations ◽  
System Of Nonlinear Equations ◽  
Numerical Tests ◽  
Programming Package ◽  
New Iterative Method

We consider a system of nonlinear equationsF(x)=0. A new iterative method for solving this problem numerically is suggested. The analytical discussions of the method are provided to reveal its sixth order of convergence. A discussion on the efficiency index of the contribution with comparison to the other iterative methods is also given. Finally, numerical tests illustrate the theoretical aspects using the programming package Mathematica.

scholarly journals On some iterative method for solving nonlinear equations

2019 ◽  
pp. 7-8
Author(s):  
Olya Kovalchuk ◽  
Myhaylo Bartish ◽  
Natalya Ogorodnyk
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Divided Difference ◽  
System Of Nonlinear Equations ◽  
Step Method ◽  
Numerical Examples

We study an iterative differential-difference three-step method for solving system of nonlinear equations, which uses, instead of the Jacobian, the sum of derivate of differentiable parts of operator and divided difference of nondifferentiable parts. The numerical examples illustrate how the methods works.

scholarly journals Multi-Step Preconditioned Newton Methods for Solving Systems of Nonlinear Equations

2017 ◽  
Author(s):  
Fayyaz Ahmad ◽  
Malik Zaka Ullah ◽  
Ali Saleh Alshomrani ◽  
Shamshad Ahmad ◽  
Aisha M. Alqahtani ◽  
...  
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Numerical Stability ◽  
Order Of Convergence ◽  
Convergence Order ◽  
Systems Of Nonlinear Equations ◽  
System Of Nonlinear Equations ◽  
Newton Methods ◽  
Rapid Convergence ◽  
Base Method

The study of different forms of preconditioners for solving a system of nonlinear equations, by using Newton’s method, is presented. The preconditioners provide numerical stability and rapid convergence with reasonable computation cost, whenever chosen accurately. Different families of iterative methods can be constructed by using a different kind of preconditioners. The multi-step iterative method consists of a base method and multi-step part. The convergence order of base method is quadratic and each multi-step add an additive factor of one in the previously achieved convergence order. Hence the convergence of order of an m-step iterative method is m + 1. Numerical simulations confirm the claimed convergence order by calculating the computational order of convergence. Finally, the numerical results clearly show the benefit of preconditioning for solving system of nonlinear equations.

Solving System of Nonlinear Equations using Genetic Algorithm

2019 ◽  
Vol 10 (4) ◽  
pp. 877-886 ◽  
Author(s):  
Chhavi Mangla ◽  
Musheer Ahmad ◽  
Moin Uddin
Keyword(s):  
Genetic Algorithm ◽  
Nonlinear Equations ◽  
System Of Nonlinear Equations

An Efficient Sixth-Order Convergent Newton-Type Iterative Method for Nonlinear Equations

2012 ◽  
Vol 220-223 ◽  
pp. 2585-2588
Author(s):  
Zhong Yong Hu ◽  
Fang Liang ◽  
Lian Zhong Li ◽  
Rui Chen
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Efficiency Index ◽  
Sixth Order ◽  
Type Method ◽  
Second Derivatives ◽  
Better Than

In this paper, we present a modified sixth order convergent Newton-type method for solving nonlinear equations. It is free from second derivatives, and requires three evaluations of the functions and two evaluations of derivatives per iteration. Hence the efficiency index of the presented method is 1.43097 which is better than that of classical Newton’s method 1.41421. Several results are given to illustrate the advantage and efficiency the algorithm.

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