A splitting method to solve a single nonlinear equation with derivative-free iterative schemes

2021 ◽  
Author(s):  
Chein-Shan Liu ◽  
Hong-Ki Hong ◽  
Tsung-Lin Lee
Keyword(s):  
Nonlinear Equation ◽  
Splitting Method ◽  
Iterative Schemes ◽  
Derivative Free

A three-step derivative free iterative method for solving a nonlinear equation

2014 ◽  
Vol 8 ◽  
pp. 4425-4431
Author(s):  
Rika Intan ◽  
M. Imran ◽  
M. D. H. Gamal
Keyword(s):  
Nonlinear Equation ◽  
Iterative Method ◽  
Derivative Free

scholarly journals Optimal Derivative-Free Root Finding Methods Based on Inverse Interpolation

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 164
Author(s):  
Moin-ud-Din Junjua ◽  
Fiza Zafar ◽  
Nusrat Yasmin
Keyword(s):  
Nonlinear Equation ◽  
Order Of Convergence ◽  
Optimal Order ◽  
Science And Engineering ◽  
Optimal Order Of Convergence ◽  
Van Der Waals Equation ◽  
First Order ◽  
Root Finding ◽  
Derivative Free ◽  
Inverse Interpolation

Finding a simple root for a nonlinear equation f ( x ) = 0 , f : I ⊆ R → R has always been of much interest due to its wide applications in many fields of science and engineering. Newton’s method is usually applied to solve this kind of problems. In this paper, for such problems, we present a family of optimal derivative-free root finding methods of arbitrary high order based on inverse interpolation and modify it by using a transformation of first order derivative. Convergence analysis of the modified methods confirms that the optimal order of convergence is preserved according to the Kung-Traub conjecture. To examine the effectiveness and significance of the newly developed methods numerically, several nonlinear equations including the van der Waals equation are tested.

scholarly journals A New Sixth-Order Steffensen-Type Iterative Method for Solving Nonlinear Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Tahereh Eftekhari
Keyword(s):  
Nonlinear Equation ◽  
Iterative Method ◽  
Nonlinear Equations ◽  
Efficiency Index ◽  
Sixth Order ◽  
New Method ◽  
Derivative Free ◽  
Better Than

Based on iterative method proposed by Basto et al. (2006), we present a new derivative-free iterative method for solving nonlinear equations. The aim of this paper is to develop a new method to find the approximation of the root α of the nonlinear equation f(x)=0. This method has the efficiency index which equals 61/4=1.5651. The benefit of this method is that this method does not need to calculate any derivative. Several examples illustrate that the efficiency of the new method is better than that of previous methods.

scholarly journals A New Derivative-Free Method to Solve Nonlinear Equations

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 583
Author(s):  
Beny Neta
Keyword(s):  
Nonlinear Equation ◽  
Nonlinear Equations ◽  
High Order ◽  
Order Derivative ◽  
Eighth Order ◽  
High Order Derivative ◽  
Derivative Free ◽  
Derivative Free Method

A new high-order derivative-free method for the solution of a nonlinear equation is developed. The novelty is the use of Traub’s method as a first step. The order is proven and demonstrated. It is also shown that the method has much fewer divergent points and runs faster than an optimal eighth-order derivative-free method.

scholarly journals Derivative Free Levenberg-Marquardt Method for Solving Fuzzy Nonlinear Equation

2021 ◽  
Vol 1115 (1) ◽  
pp. 012002
Author(s):  
A U Omesa ◽  
I M Sulaiman ◽  
M Mamat ◽  
M Y Waziri ◽  
A Shadi ◽  
...  
Keyword(s):  
Nonlinear Equation ◽  
Marquardt Method ◽  
Derivative Free ◽  
Levenberg Marquardt

scholarly journals Numerical Scheme for Finding Roots of Interval-Valued Fuzzy Nonlinear Equation with Application in Optimization

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Ahmed Elmoasry ◽  
Mudassir Shams ◽  
Naveed Yaqoob ◽  
Nasreen Kausar ◽  
Yaé Ulrich Gaba ◽  
...  
Keyword(s):  
Nonlinear Equation ◽  
Numerical Scheme ◽  
Order Of Convergence ◽  
Numerical Test ◽  
Real Life ◽  
Test Problems ◽  
Parametric Form ◽  
Iterative Schemes ◽  
Research Article ◽  
Interval Valued

In this research article, we propose efficient numerical iterative methods for estimating roots of interval-valued trapezoidal fuzzy nonlinear equations. Convergence analysis proves that the order of convergence of numerical schemes is 3. Some real-life applications are considered from optimization as numerical test problems which contain interval-valued trapezoidal fuzzy quantities in parametric form. Numerical illustrations are given to show the dominance efficiency of the newly constructed iterative schemes as compared to existing methods in literature.

scholarly journals King-Type Derivative-Free Iterative Families: Real and Memory Dynamics

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
F. I. Chicharro ◽  
A. Cordero ◽  
J. R. Torregrosa ◽  
M. P. Vassileva
Keyword(s):  
Quadratic Polynomials ◽  
The Real ◽  
Iterative Schemes ◽  
Derivative Free ◽  
Parametric Plane ◽  
Real Behavior ◽  
Order Four ◽  
Real Stability ◽  
With Memory ◽  
Parametric Class

A biparametric family of derivative-free optimal iterative methods of order four, for solving nonlinear equations, is presented. From the error equation of this class, different families of iterative schemes with memory can be designed increasing the order of convergence up to six. The real stability analysis of the biparametric family without memory is made on quadratic polynomials, finding areas in the parametric plane with good performance. Moreover, in order to study the real behavior of the parametric class with memory, we associate it with a discrete multidimensional dynamical system. By analyzing the fixed and critical points of its vectorial rational function, we can select those methods with best stability properties.

scholarly journals On highly efficient derivative-free family of numerical methods for solving polynomial equation simultaneously

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mudassir Shams ◽  
Naila Rafiq ◽  
Nasreen Kausar ◽  
Praveen Agarwal ◽  
Choonkil Park ◽  
...  
Keyword(s):  
Numerical Methods ◽  
Computational Cost ◽  
Polynomial Equation ◽  
Polynomial Equations ◽  
Order Convergence ◽  
Numerical Examples ◽  
Iterative Schemes ◽  
Highly Efficient ◽  
Derivative Free ◽  
Solving Polynomial Equation

AbstractA highly efficient new three-step derivative-free family of numerical iterative schemes for estimating all roots of polynomial equations is presented. Convergence analysis proved that the proposed simultaneous iterative method possesses 12th-order convergence locally. Numerical examples and computational cost are given to demonstrate the capability of the method presented.

scholarly journals A General Class of Derivative Free Optimal Root Finding Methods Based on Rational Interpolation

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Fiza Zafar ◽  
Nusrat Yasmin ◽  
Saima Akram ◽  
Moin-ud-Din Junjua
Keyword(s):  
General Class ◽  
Order Of Convergence ◽  
Rational Interpolation ◽  
Optimal Order ◽  
Optimal Order Of Convergence ◽  
Iterative Schemes ◽  
Root Finding ◽  
New Methods ◽  
Derivative Free ◽  
Special Cases

We construct a new general class of derivative freen-point iterative methods of optimal order of convergence2n-1using rational interpolant. The special cases of this class are obtained. These methods do not need Newton’s iterate in the…first step of their iterative schemes. Numerical computations are presented to show that the new methods are efficient and can be seen as better alternates.

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