Modified Abbasbandy’s method free from second derivative for solving nonlinear equations (original) (raw)

Deprived of Second Derivative Iterated Method for Solving Nonlinear Equations

Proceedings of the Pakistan Academy of Sciences: A. Physical and Computational Sciences, 2021

Non-linear equations are one of the most important and useful problems, which arises in a varied collection of practical applications in engineering and applied sciences. For this purpose, in this paper has been developed an iterative method with deprived of second derivative for the solution of non-linear problems. The developed deprived of second derivative iterative method is convergent quadratically, and which is derived from Newton Raphson Method and Taylor series. The numerical results of the developed method are compared with the Newton Raphson Method and Modified Newton Raphson Method. From graphical representation and numerical results, it has been observed that the deprived of second derivative iterative method is more appropriate and suitable as accuracy and iteration perception by the valuation of Newton Raphson Method and Modified Newton Raphson Method for estimating a non-linear problem.

Some New Derivative Free Methods for Solving Nonlinear Equations

Academic Research International

This paper proposes two new iterative methods for solving nonlinear equations. In comparison to the classical Newton’s method, the new proposed methods do not use derivatives; furthermore only two evaluations of the function are needed per iteration. Using the methods proposed, when the starting value is selected close to the root, the order of convergence is 2. The development of the method allows you to achieve classical methods such as secant and Steffensen’s as an alternative to the usual process. The numerical examples show that the proposed methods have the same performance as Newton’s method with the advantage of being derivative free. In comparison to other methods which are derivative free, these methods are more efficient.

Comparison of Some Iterative Methods of Solving Nonlinear Equations

International Journal of Theoretical and Applied Mathematics, 2018

This work focuses on nonlinear equation (x) = 0, it is noted that no or little attention is given to nonlinear equations. The purpose of this work is to determine the best method of solving nonlinear equations. The work outlined four methods of solving nonlinear equations. Unlike linear equations, most nonlinear equations cannot be solved in finite number of steps. Iterative methods are being used to solve nonlinear equations. The cost of solving nonlinear equations problems depend on both the cost per iteration and the number of iterations required. Derivations of each of the methods were obtained. An example was illustrated to show the results of all the four methods and the results were collected, tabulated and analyzed in terms of their errors and convergence respectively. The results were also presented in form of graphs. The implication is that the higher the rate of convergence determines how fast it will get to the approximate root or solution of the equation. Thus, it was recommended that the Newton's method is the best method of solving the nonlinear equation f(x) = 0 containing one variable because of its high rate of convergence.

Some new multi-step derivative-free iterative methods for solving nonlinear equations

Işık University Press, 2020

In this paper, we use the system of coupled equation involving auxiliary function with decomposition technique. We also use finite difference technique to suggest and analyze some new derivative-free iterative methods for solving nonlinear equations. Several examples are given to check the performance of developed methods numerically as well as graphically. This technique can be implemented to suggest a wide class of new derivative-free iterative methods for solving nonlinear equations.

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 solutions of higher order nonlinear boundary value problems by new iterative method

Applied Mathematical Sciences, 2013

In this work, we present the approximate solutions of higher order nonlinear boundary value problems by an efficient numerical algorithm. The New Iterative Method (NIM) will by used to find such solutions. The solutions thus obtained by NIM, are in the form of rapidly convergent series. The approach developed is tested through examples, which gives the stability and efficiency of the proposed algorithm.

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.

High order iterative methods without derivatives for solving nonlinear equations

Applied Mathematics and Computation, 2007

The new second-order and third-order iterative methods without derivatives are presented for solving nonlinear equations; the iterative formulae based on the homotopy perturbation method are deduced and their convergences are provided. Finally, some numerical experiments show the efficiency of the theoretical results for the above methods.

Two Higher Order Iterative Methods for Solving Nonlinear Equations

Journal of the Institute of Engineering

The main purpose of this paper is to derive two higher order iterative methods for solving nonlinear equations as variants of Mir, Ayub and Rafiq method. These methods are free from higher order derivatives. We obtain these methods by amalgamating Mir, Ayub and Rafiq method with standard secant method and modified secant method given by Amat and Busquier. The order of convergence of new variants are four and six. Also, numerical examples are given to compare the performance of newly introduced methods with the similar existing methods. 2010 AMS Subject Classification: 65H05 Journal of the Institute of Engineering, 2018, 14(1): 179-187

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.