scholarly journals Second Derivative Free Eighteenth Order Convergent Method for Solving Non-Linear Equations

2017 ◽  
Vol 10 (04) ◽  
pp. 829-835
Author(s):  
V.B. Kumar Vatti ◽  
Ramadevi Sri ◽  
M.S.Kumar Mylapalli
Keyword(s):  
Linear Equations ◽  
Efficiency Index ◽  
Subject Classification ◽  
New Method ◽  
Second Derivative ◽  
Numerical Examples ◽  
Derivative Free ◽  
Convergent Method ◽  
And Performance ◽  
Non Linear Equations

In this paper, the Eighteenth Order Convergent Method (EOCM) developed by Vatti et.al is considered and this method is further studied without the presence of second derivative. It is shown that this method has same efficiency index as that of EOCM. Several numerical examples are given to illustrate the efficiency and performance of the new method. AMS Subject Classification: 41A25, 65K05, 65H05.

scholarly journals Eighteenth Order Convergent Method for Solving Non-Linear Equations

2017 ◽  
Vol 10 (1) ◽  
pp. 144-150 ◽  
Author(s):  
V.B Vatti ◽  
Ramadevi Sri ◽  
M.S Mylapalli
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Linear Equations ◽  
Subject Classification ◽  
Order Convergence ◽  
Numerical Examples ◽  
Convergent Method ◽  
Non Linear Equations

In this paper, we suggest and discuss an iterative method for solving nonlinear equations of the type f(x)=0 having eighteenth order convergence. This new technique based on Newton’s method and extrapolated Newton’s method. This method is compared with the existing ones through some numerical examples to exhibit its superiority. AMS Subject Classification: 41A25, 65K05, 65H05.

scholarly journals A derivative free globally convergent method and its deformations

2021 ◽  
Author(s):  
Manoj Kumar Singh ◽  
Arvind K. Singh
Keyword(s):  
Difference Operator ◽  
Linear Equations ◽  
Numerical Test ◽  
Test Functions ◽  
Globally Convergent ◽  
Forward Difference ◽  
Derivative Free ◽  
Fractal Patterns ◽  
Convergent Method ◽  
Non Linear Equations

AbstractThe motive of the present work is to introduce and investigate the quadratically convergent Newton’s like method for solving the non-linear equations. We have studied some new properties of a Newton’s like method with examples and obtained a derivative-free globally convergent Newton’s like method using forward difference operator and bisection method. Finally, we have used various numerical test functions along with their fractal patterns to show the utility of the proposed method. These patterns support the numerical results and explain the compactness regarding the convergence, divergence and stability of the methods to different roots.

A New Method for Solving the Constraint Multibody System Dynamic Equation

2011 ◽  
Vol 345 ◽  
pp. 361-364
Author(s):  
Ding Xuan Zhao ◽  
Yu Xin Cui ◽  
Tao Ni ◽  
Ying Zhao ◽  
Chao Fei Wang
Keyword(s):  
Dynamic Equation ◽  
Multibody System ◽  
Linear Equations ◽  
Constraint Equation ◽  
System Dynamic ◽  
New Method ◽  
Taylor Formula ◽  
Second Derivative ◽  
System Constraint ◽  
Non Linear Equations

Aiming at the problem of solving the constraint multibody system dynamic equation, a new method is proposed. This method takes the function of general coordinates to replace the second derivative of the general coordinates in the dynamic equation according to Taylor formula, and considers the converted dynamic equation and system constraint equation as a system of non-linear equations to find the solution by Newton method. Experimental results show that the proposed method is efficient and accurate for solving the constraint multibody system dynamic equation.

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.

A new method to solve non-linear equations

1994 ◽  
Vol 50 (2) ◽  
pp. 75-79
Author(s):  
T. Sony Roy ◽  
G. Athithan ◽  
M.S. Ganagi ◽  
A. Sivasankara Reddy
Keyword(s):  
Linear Equations ◽  
New Method ◽  
Non Linear ◽  
Non Linear Equations

scholarly journals An Iterative Hybrid Algorithm for Roots of Non-Linear Equations

Eng ◽  
2021 ◽  
Vol 2 (1) ◽  
pp. 80-98
Author(s):  
Chaman Lal Sabharwal
Keyword(s):  
Hybrid Algorithm ◽  
Analytic Solution ◽  
Linear Equations ◽  
Root Finding ◽  
Engineering Sciences ◽  
Non Linear ◽  
False Position ◽  
Newton Raphson ◽  
And Performance ◽  
Non Linear Equations

Finding the roots of non-linear and transcendental equations is an important problem in engineering sciences. In general, such problems do not have an analytic solution; the researchers resort to numerical techniques for exploring. We design and implement a three-way hybrid algorithm that is a blend of the Newton–Raphson algorithm and a two-way blended algorithm (blend of two methods, Bisection and False Position). The hybrid algorithm is a new single pass iterative approach. The method takes advantage of the best in three algorithms in each iteration to estimate an approximate value closer to the root. We show that the new algorithm outperforms the Bisection, Regula Falsi, Newton–Raphson, quadrature based, undetermined coefficients based, and decomposition-based algorithms. The new hybrid root finding algorithm is guaranteed to converge. The experimental results and empirical evidence show that the complexity of the hybrid algorithm is far less than that of other algorithms. Several functions cited in the literature are used as benchmarks to compare and confirm the simplicity, efficiency, and performance of the proposed method.

scholarly journals Comparison of Proposed and Existing Fourth Order Schemes for Solving Non-linear Equations

2019 ◽  
pp. 1-7
Author(s):  
Khushbu Rajput ◽  
Asif Ali Shaikh ◽  
Sania Qureshi
Keyword(s):  
Nonlinear Equations ◽  
Fourth Order ◽  
Numerical Approximation ◽  
Real Root ◽  
Graphical Representation ◽  
Linear Equations ◽  
Order Convergence ◽  
Derivative Free ◽  
Non Linear Equations ◽  
Number Of Iterations

This paper, investigates the comparison of the convergence behavior of the proposed scheme and existing schemes in literature. While all schemes having fourth-order convergence and derivative-free nature. Numerical approximation demonstrates that the proposed schemes are able to attain up to better accuracy than some classical methods, while still significantly reducing the total number of iterations. This study has considered some nonlinear equations (transcendental, algebraic and exponential) along with two complex mathematical models. For better analysis graphical representation of numerical methods for finding the real root of nonlinear equations with varying parameters has been included. The proposed scheme is better in reducing error rapidly, hence converges faster as compared to the existing schemes.

scholarly journals Five-point thirty-two optimal order iterative method for solving non-linear equations

2021 ◽  
Vol 25 (Spec. issue 2) ◽  
pp. 401-409
Author(s):  
Malik Ullah ◽  
Fayyaz Ahmad
Keyword(s):  
Iterative Method ◽  
Linear Equations ◽  
Initial Guess ◽  
Convergence Order ◽  
Optimal Order ◽  
Order Convergence ◽  
Derivative Free ◽  
Non Linear ◽  
High Order Convergence ◽  
Non Linear Equations

A five-point thirty-two convergence order derivative-free iterative method to find simple roots of non-linear equations is constructed. Six function evaluations are performed to achieve optimal convergence order 26-1 = 32 conjectured by Kung and Traub [1]. Secant approximation to the derivative is computed around the initial guess. High order convergence is attained by constructing polynomials of quotients for functional values.

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