New Three-Steps Iterative Method for Solving Nonlinear Equations (original) (raw)

Some quadrature based three-step iterative methods for non-linear equations

Applied Mathematics and Computation, 2007

In this paper, we present three-step iterative method for solving nonlinear equations. The convergence analysis of the method is discussed. It is established that the new method has convergence order eight. Numerical examples are given to test the efficiency and performance of the method. Numerical tests show that the new method is comparable with the well known existing methods and in many cases gives better results. Our results can be considered as an improvement and refinement of the previously known results in the literature.

An efficient three-step iterative method with sixth-order convergence for solving nonlinear equations

International Journal of Computer Mathematics, 2007

The aim of this paper is to construct an e¢ cient iterative method to solve nonlinear equations. This method is obtained from M. Javidi's method (Appl. Math. Comput. 193 (2007) 360-365), which is third-order. The convergence order of new method is established to six and the e¢ ciency index is 1.5651. The Proposed method is compared with the second, third and sixth order methods. Some numerical test problems are given to show the accuracy and fast convergence of the proposed method.

Three New Iterative Methods for Solving Nonlinear Equations

In this paper, we present a family of new iterative methods for solving nonlinear equations based on Newton's method. The order of convergence and corresponding error equations of the obtained iteration formulae are derived analytically and with the help of Maple. Some numerical examples are given to illustrate the efficiency of the presented methods, so one would be able to compare the results of the same problems obtained by applying different methods, and the advantage of the new methods can be recognized.

Numerical comparison of iterative methods for solving nonlinear equations

Applied Mathematics and Computation, 2006

In this paper, we suggest some new predictor-corrector type iterative method for solving nonlinear equations by combining the well known Regula Falsi and Newton method. Numerical experiments show that new predictor-corrector type methods perform better than the previously known methods.

Quadrature based three-step iterative method for non-linear equations 1

2010

In this paper, we present three-step quadrature based iterative method for solving non-linear equations. The convergence analysis of the method is discussed. It is established that the new method has convergence order eight. Numerical tests show that the new method is comparable with the well known existing methods and in many cases gives better results. Our results can be considered as an improvement and reflnement of the previously known results in the literature.

New Third-order Iterative Method for Solving Nonlinear Equations.

In this paper, we present a new third-order iterative method for solving nonlinear equations. The new method is based on Newton-Raphson method and Taylor series method. The efficiency of the method is tested on several numerical examples. It is observed that the method is comparable with the well-known existing methods and in many cases gives better results.

An Efficient Three-step Iterative Methods Based on Bernstein Quadrature Formula for Solving Nonlinear Equations

BASRA JOURNAL OF SCIENCE

In this study, we suggest and analyze two new one-parameter families of an efficient iterative methods free from higher derivatives for solving nonlinear equations based on Newton theorem of calculus and Bernstein quadrature formula, Bernoulli polynomial basis, Taylor’s expansion and some numerical techniques. We prove that the new iterative methods reach orders of convergence ten with six and eight with four functional evaluations per iteration, which implies that the efficiency index of the new iterative methods is (10)1/6 1.4678 and (8)1/4 1.6818 respectively. Numerical examples are provided to show the efficiency and performance of our iterative methods, compare to Newton’s method and other relevant methods.

A Family of Combined Iterative Methods for Solving Nonlinear Equations

In this article we construct some higher-order modifications of Newton's method for solving nonlinear equations, which is based on the undetermined coefficients. This construction can be applied to any iteration formula. It can be found that per iteration the resulting methods add only one additional function evaluation, their order of convergence can be increased by two or three units. Higher order convergence of our methods is proved and corresponding asymptotic error constants are expressed. Numerical examples, obtained using Matlab with high precision arithmetic, are shown to demonstrate the convergence and efficiency of the combined iterative methods. It is found that the combined iterative methods produce very good results on tested examples, compared to the results produced by the existing higher order schemes in the related literature.