scholarly journals Two Higher Order Iterative Methods for Solving Nonlinear Equations

2018 ◽  
Vol 14 (1) ◽  
pp. 179-187
Author(s):  
Jivandhar Jnawali ◽  
Chet Raj Bhatta
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
Higher Order ◽  
Secant Method ◽  
Subject Classification ◽  
Numerical Examples ◽  
Ams Subject Classification

 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

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 New Modified Newton Type Iterative Methods

2021 ◽  
Vol 2 (1) ◽  
pp. 17-24
Author(s):  
Jivandhar Jnawali
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
Single Variable ◽  
Numerical Examples

In this work, we present two Newton type iterative methods for finding the solution of nonlinear equations of single variable. One is obtained as variant of McDougall and Wotherspoon method, and another is obtained by amalgamation of Potra and Pta’k method and our newly introduced method. The order of convergence of these methods are 1 + √2 and 3.5615. Some numerical examples are given to compare the performance of these methods with some similar 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 New Iterative Methods for Solving Nonlinear Equations and Their Basins of Attraction

2022 ◽  
Vol 21 ◽  
pp. 9-16
Author(s):  
O. Ababneh
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Newton's Method ◽  
Order Of Convergence ◽  
Iterative Algorithms ◽  
Basins Of Attraction ◽  
Second Derivative ◽  
Numerical Examples ◽  
Convergence Results ◽  
Modified Newton’S Method

The purpose of this paper is to propose new modified Newton’s method for solving nonlinear equations and free from second derivative. Convergence results show that the order of convergence is four. Several numerical examples are given to illustrate that the new iterative algorithms are effective.In the end, we present the basins of attraction to observe the fractal behavior and dynamical aspects of the proposed algorithms.

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 Numerical Algorithms for Finding Zeros of Nonlinear Equations and Their Dynamical Aspects

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Amir Naseem ◽  
M. A. Rehman ◽  
Thabet Abdeljawad ◽  
Francisco Balibrea
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
Numerical Algorithms ◽  
One Dimension ◽  
Second Derivative ◽  
Numerical Examples ◽  
Derivative Free ◽  
Interpolation Technique ◽  
Taylor’S Series

In this paper, we developed two new numerical algorithms for finding zeros of nonlinear equations in one dimension and one of them is second derivative free which has been removed using the interpolation technique. We derive these algorithms with the help of Taylor’s series expansion and Golbabai and Javidi’s method. The convergence analysis of these algorithms is discussed. It is established that the newly developed algorithms have sixth order of convergence. Several numerical examples have been solved which prove the better efficiency of these algorithms as compared to other well-known iterative methods of the same kind. Finally, the comparison of polynomiographs generated by other well-known iterative methods with our developed algorithms has been made which reflects their dynamical aspects.

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.

scholarly journals On Some Iterative Methods with Memory and High Efficiency Index for Solving Nonlinear Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Tahereh Eftekhari
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
High Efficiency ◽  
Efficiency Index ◽  
Order Convergence ◽  
Eighth Order ◽  
Additional Function ◽  
Numerical Comparisons ◽  
With Memory

Based on iterative methods without memory of eighth-order convergence proposed by Thukral (2012), some iterative methods with memory and high efficiency index are presented. We show that the order of convergence is increased without any additional function evaluations. Numerical comparisons are made to show the performance of the presented methods.

scholarly journals Metode Iterasi Tiga Langkah untuk Menyelesaikan Persamaan NonLinear dengan Menggunakan Matlab

2019 ◽  
Vol 4 (2) ◽  
pp. 34
Author(s):  
Deasy Wahyuni ◽  
Elisawati Elisawati
Keyword(s):  
Numerical Simulations ◽  
Nonlinear Equations ◽  
Newton Method ◽  
Iteration Method ◽  
Newton's Method ◽  
Order Of Convergence ◽  
Higher Order ◽  
Convergence Order ◽  
Matlab Program ◽  
Analytical Results

Newton method is one of the most frequently used methods to find solutions to the roots of nonlinear equations. Along with the development of science, Newton's method has undergone various modifications. One of them is the hasanov method and the newton method variant (vmn), with a higher order of convergence. In this journal focuses on the three-step iteration method in which the order of convergence is higher than the three methods. To find the convergence order of the three-step iteration method requires a program that can support the analytical results of both methods. One of them using the help of the matlab program. Which will then be compared with numerical simulations also using the matlab program.  Keywords : newton method, newton method variant, Hasanov Method and order of convergence

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