Some new two step iterative methods for solving nonlinear equations using Steffensen’s method (original) (raw)

New Derivative Free Iterative Method ’ S for Solving Nonlinear Equations Using Steffensen ’ S Method

2016

In this paper, we introduce the comparative study of derivative free new two step iterative method for finding the zeros of the nonlinear equation = 0 without the evaluation of the derivatives . It is established that the new method has convergence order three. The efficiency index of new method is equal to 1.442. The Convergence and error analysis are given. Numerical comparisons are made with other existing methods to show the performance of the presented methods.

Some Steffensen-type iterative schemes for the approximate solution of nonlinear equations

Miskolc Mathematical Notes, 2021

In this paper, we suggest some new and efficient iterative methods for solving nonlinear equations f (x) = 0. These methods are free from derivatives having high order of convergence. We also give some examples to illustrate the efficiency of these methods. Finally, numerical tests confirm the theoretical results and allow us to compare these variants with the classical Steffensen's method. These new methods can be considered as alternative of existing derivative-free methods.

New Two step Iterative Methods for Solving Nonlinear 1

In this paper, we have suggested and analyzed a new two-step type iterative methods for solving nonlinear equations of the type. We show that this new two-step method is cubic convergence method. It is proved that this method is better than the Newton method and all results in (Soheili et al., 2008). Several examples are given to illustrate the efficiency of this new method and its comparison with other methods. This method can se considered as a significant improvement of the Newton method and its variant forms.

Numerical Study of Some Iterative Methods for Solving Nonlinear Equations

IJEST, 2016

In this paper we introduce, numerical study of some iterative methods for solving non linear equations. Many iterative methods for solving algebraic and transcendental equations is presented by the different formulae. Using bisection method , secant method and the Newton's iterative method and their results are compared. The software, matlab 2009a was used to find the root of the function for the interval [0,1]. Numerical rate of convergence of root has been found in each calculation. It was observed that the Bisection method converges at the 47 iteration while Newton and Secant methods converge to the exact root of 0.36042170296032 with error level at the 4th and 5th iteration respectively. It was also observed that the Newton method required less number of iteration in comparison to that of secant method. However, when we compare performance, we must compare both cost and speed of convergence [6]. It was then concluded that of the three methods considered, Secant method is the most effective scheme. By the use of numerical experiments to show that secant method are more efficient than others.

A new iterative method for solving nonlinear equations

Applied Mathematics and Computation, 2006

In this study, a new root-finding method for solving nonlinear equations is proposed. This method requires two starting values that do not necessarily bracketing a root. However, when the starting values are selected to be close to a root, the proposed method converges to the root quicker than the secant method. Another advantage over all iterative methods is that; the proposed method usually converges to two distinct roots when the given function has more than one root, that is, the odd iterations of this new technique converge to a root and the even iterations converge to another root. Some numerical examples, including a sine-polynomial equation, are solved by using the proposed method and compared with results obtained by the secant method; perfect agreements are found.

Two-step iterative methods for nonlinear equations

Applied Mathematics and Computation, 2006

In recent years several iterative methods have been suggested and analyzed for solving nonlinear equation f(x) = 0. All these methods can be classified as one-step and two-step methods. In this paper, we consider and analyze two-step iterative methods for solving nonlinear equations. It is shown that two-step iterative methods are more efficient than one-step methods including Newton method. Several numerical examples are given to illustrate this comparison. Our results can be viewed as important refinement and improvement of the previously known results.

Derivative Free Three-Step Iterative Method to Solve Nonlinear Equations

INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH

This article discusses a derivative free three-step iterative method to solve a nonlinear equation using Steffensen method, after approximating the derivative in the method proposed by Abro et al. [Appl. Math. Comput.,55(2019),516-536] by a divided difference method. We show analytically that the method is of order sixth under a condition and for each iteration it requires three function evaluations. Numerical experiments show that the new method is comparable with other discussed method.

Modified Iterative Method for Solving Nonlinear Equation

In this paper, we present new one- and two-steps iterative methods for solving nonlinear equation f(x)=0. It is proved here that the iterative methods converge of order three and six respectively. Several numerical examples are given to illustrate the performance and to show that the iterative methods in this paper give better result than the compared methods

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.

New Three-Steps Iterative Method for Solving Nonlinear Equations

Abstract: In this paper, we proposed a new three steps iterative method of order six for solving nonlinear equations. The method uses predictor–corrector technique, is constructed based on a Newton iterative method and the weight combination of mid-point with Simpson quadrature formulas. Several numerical examples are given to illustrate the efficiency and performance of the iterative methods; the methods are also compared with well known existing iterative method. Keywords: Newton method, Order of convergence, Predictor-Corrector method, Quadrature method