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.

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 Decomposition Technique and a Family of Efficient Schemes for Nonlinear Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Farooq Ahmed Shah ◽  
Maslina Darus ◽  
Imran Faisal ◽  
Muhammad Arsalan Shafiq
Keyword(s):  
Applied Sciences ◽  
Iterative Methods ◽  
Nonlinear Equations ◽  
Decomposition Technique ◽  
Unified Framework ◽  
New Methods ◽  
New Family ◽  
And Performance

Various problems of pure and applied sciences can be studied in the unified framework of nonlinear equations. In this paper, a new family of iterative methods for solving nonlinear equations is developed by using a new decomposition technique. The convergence of the new methods is proven. For the implementation and performance of the new methods, some examples are solved and the results are compared with some existing 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.

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 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.

Some New Iterative Techniques for the Problems Involving Nonlinear Equations

2019 ◽  
Vol 17 (07) ◽  
pp. 1950037 ◽  
Author(s):  
Faisal Ali ◽  
Waqas Aslam ◽  
Arif Rafiq
Keyword(s):  
Mathematical Models ◽  
Iterative Methods ◽  
Nonlinear Equations ◽  
Graphical Analysis ◽  
Decomposition Technique ◽  
Convergence Criteria ◽  
Iterative Techniques ◽  
New Methods

We develop some new iterative methods, using decomposition technique, for solving the problems which involve nonlinear equations. Importantly, these methods include the generalization of some well-known existing methods. We prove the convergence criteria of our newly proposed methods. Various test examples are considered to validate the efficiency of our new methods. We also give the numerical as well as graphical analysis for two mathematical models to endorse the performance of these methods.

scholarly journals Some Class of Third- and Fourth-Order Iterative Methods for Solving Nonlinear Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-17 ◽  
Author(s):  
J. P. Jaiswal
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Fourth Order ◽  
Basins Of Attraction ◽  
Order Method ◽  
Third Order ◽  
Numerical Examples ◽  
Multivariate Extension ◽  
New Class ◽  
Fourth Order Method

The object of the present work is to give the new class of third- and fourth-order iterative methods for solving nonlinear equations. Our proposed third-order method includes methods of Weerakoon and Fernando (2000), Homeier (2005), and Chun and Kim (2010) as particular cases. The multivariate extension of some of these methods has been also deliberated. Finally, some numerical examples are given to illustrate the performances of our proposed methods by comparing them with some well existing third- and fourth-order methods. The efficiency of our proposed fourth-order method over some fourth-order methods is also confirmed by basins of attraction.

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