scholarly journals Novel Three Order Methods for Solving a System of Nonlinear Equations

2012 ◽  
Vol 2 ◽  
pp. 1-12 ◽  
Author(s):  
M.Q. Khirallah ◽  
M.A. Hafiz
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Newton Method ◽  
System Of Nonlinear Equations ◽  
Numerical Examples ◽  
And Performance ◽  
Predictor Corrector ◽  
New Algorithms

In this paper, we suggest and study Simpson's formula, and Newton's two, three and four Cosed formulas iterative methods for solving the system of nonlinear equations by using Predictor-Corrector of Newton method. We present four new algorithms for solving the system of nonlinear equations (SNLE). We prove that these new algorithms have convergence. Several numerical examples are given to illustrate the efficiency and performance of the new iterative methods. These new algorithms may be viewed as an extensions and generalizations of the existing methods for solving the system of nonlinear equations.

scholarly journals Some New Iterative Methods for Nonlinear Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor ◽  
Eisa Al-Said ◽  
Muhammad Waseem
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Fourth Order ◽  
System Of Equations ◽  
Decomposition Technique ◽  
Methods Comparison ◽  
Numerical Examples ◽  
New Methods ◽  
And Performance

We suggest and analyze some new iterative methods for solving the nonlinear equationsf(x)=0using the decomposition technique coupled with the system of equations. We prove that new methods have convergence of fourth order. Several numerical examples are given to illustrate the efficiency and performance of the new methods. Comparison with other similar methods is given.

Higher Order Convergent Newton Type Iterative Methods

2018 ◽  
Vol 1 (2) ◽  
pp. 32-39
Author(s):  
Jivandhar Jnawali
Keyword(s):  
Numerical Methods ◽  
Iterative Methods ◽  
Nonlinear Equations ◽  
Newton Method ◽  
Order Of Convergence ◽  
Higher Order ◽  
Predictor Corrector ◽  
Appl Math

Newton method is one of the most widely used numerical methods for solving nonlinear equations. McDougall and Wotherspoon [Appl. Math. Lett., 29 (2014), 20-25] modified this method in predictor-corrector form and get an order of convergence 1+√2. More on the PDF

scholarly journals Modified Homotopy Perturbation Technique for the Approximate Solution of Nonlinear Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Farooq Ahmed Shah
Keyword(s):  
Approximate Solution ◽  
Iterative Methods ◽  
Nonlinear Equations ◽  
Homotopy Perturbation Method ◽  
Perturbation Technique ◽  
Numerical Examples ◽  
Homotopy Perturbation ◽  
New Methods ◽  
And Performance ◽  
Homotopy Perturbation Technique

We use a new modified homotopy perturbation method to suggest and analyze some new iterative methods for solving nonlinear equations. This new modification of the homotopy method is quite flexible. Various numerical examples are given to illustrate the efficiency and performance of the new methods. These new iterative methods may be viewed as an addition and generalization of the existing methods for solving nonlinear equations.

scholarly journals A New Three-Step Class of Iterative Methods for Solving Nonlinear Systems

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1221 ◽  
Author(s):  
Raudys R. Capdevila ◽  
Alicia Cordero ◽  
Juan R. Torregrosa
Keyword(s):  
Nonlinear Systems ◽  
Weight Function ◽  
Iterative Methods ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
Systems Of Equations ◽  
Nonlinear Systems Of Equations ◽  
Numerical Examples ◽  
New Class ◽  
And Performance

In this work, a new class of iterative methods for solving nonlinear equations is presented and also its extension for nonlinear systems of equations. This family is developed by using a scalar and matrix weight function procedure, respectively, getting sixth-order of convergence in both cases. Several numerical examples are given to illustrate the efficiency and performance of the proposed methods.

NEW ITERATIVE METHODS FOR SOLVING INTEGRAL EQUATIONS

2011 ◽  
Vol 25 (32) ◽  
pp. 4655-4660
Author(s):  
MUHAMMAD ASLAM NOOR ◽  
KHALIDA INAYAT NOOR ◽  
EISA AL-SAID
Keyword(s):  
Integral Equations ◽  
Iterative Methods ◽  
Nonlinear Equations ◽  
New Method ◽  
Decomposition Technique ◽  
Numerical Examples ◽  
And Performance

In this paper, we use the decomposition technique of Noor and Noor [M. A. Noor and K. I. Noor, Three-step iterative methods for nonlinear equations, preprint (2006)] to suggest and analyze a new iterative methods for solving the integral equations. Our method of developing this new method is very simple as compared with other methods. Several numerical examples are given to illustrate the efficiency and performance of the new method. Results reveal that the proposed method is very effective and simple. Our method can be considered as an improvement of the existing methods.

Extended conjugate gradient squared and conjugate residual squared methods for solving the generalized coupled Sylvester tensor equations

2020 ◽  
pp. 014233122093238
Author(s):  
Eisa Khosravi Dehdezi ◽  
Saeed Karimi
Keyword(s):  
Iterative Methods ◽  
Conjugate Gradient ◽  
Numerical Examples ◽  
New Methods ◽  
Conjugate Gradient Squared ◽  
And Performance ◽  
Tensor Computations ◽  
Conjugate Residual

In this paper, two attractive iterative methods – conjugate gradient squared (CGS) and conjugate residual squared (CRS) – are extended to solve the generalized coupled Sylvester tensor equations [Formula: see text]. The proposed methods use tensor computations with no maricizations involved. Also, some properties of the new methods are presented. Finally, several numerical examples are given to compare the efficiency and performance of the proposed methods with some existing algorithms.

scholarly journals Three New Optimal Fourth-Order Iterative Methods to Solve Nonlinear Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Gustavo Fernández-Torres ◽  
Juan Vásquez-Aquino
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Fourth Order ◽  
Newton’S Method ◽  
Newton's Method ◽  
Classical Method ◽  
Multiple Roots ◽  
Order Convergence ◽  
Numerical Examples ◽  
Optimal Methods

We present new modifications to Newton's method for solving nonlinear equations. The analysis of convergence shows that these methods have fourth-order convergence. Each of the three methods uses three functional evaluations. Thus, according to Kung-Traub's conjecture, these are optimal methods. With the previous ideas, we extend the analysis to functions with multiple roots. Several numerical examples are given to illustrate that the presented methods have better performance compared with Newton's classical method and other methods of fourth-order convergence recently published.

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.

Accelerated iterative methods for finding solutions of a system of nonlinear equations

2007 ◽  
Vol 190 (2) ◽  
pp. 1815-1823 ◽  
Author(s):  
Miquel Grau-Sánchez ◽  
Josep M. Peris ◽  
José M. Gutiérrez
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
System Of Nonlinear Equations
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