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.

scholarly journals Basic Steffensen's Method of Higher-Order Convergence

2021 ◽  
Vol 8 (4) ◽  
pp. 184-191
Author(s):  
Ola A. Ashour
Keyword(s):  
Fourth Order ◽  
Linear Equations ◽  
Higher Order ◽  
Order Convergence ◽  
Steffensen’S Method ◽  
Non Linear ◽  
Higher Order Convergence ◽  
Non Linear Equations

In this paper, we introduce a new analog of a variant of Steffensen's method of fourth-order convergence for solving non-linear equations based on the q-deference operator.

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.

scholarly journals Three New Optimal Fourth-Order Iterative Methods to Solve Nonlinear Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Gustavo Fernández-Torres ◽  
Juan Vásquez-Aquino
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Fourth Order ◽  
Newton’S Method ◽  
Newton's Method ◽  
Classical Method ◽  
Multiple Roots ◽  
Order Convergence ◽  
Numerical Examples ◽  
Optimal Methods

We present new modifications to Newton's method for solving nonlinear equations. The analysis of convergence shows that these methods have fourth-order convergence. Each of the three methods uses three functional evaluations. Thus, according to Kung-Traub's conjecture, these are optimal methods. With the previous ideas, we extend the analysis to functions with multiple roots. Several numerical examples are given to illustrate that the presented methods have better performance compared with Newton's classical method and other methods of fourth-order convergence recently published.

The Arithmetic of Field Equations

1953 ◽  
Vol 4 (2) ◽  
pp. 205-230 ◽  
Author(s):  
A. Thom
Keyword(s):  
Fourth Order ◽  
Linear Equations ◽  
Field Equations ◽  
Solution Of Equations ◽  
Non Linear ◽  
Propagation Of Errors ◽  
Fourth Order Equations ◽  
Non Linear Equations ◽  
Poisson Type

SummaryThe paper describes in detail an older method than Relaxation of approximating to the solution of equations of the Laplace and Poisson type. The corresponding fourth order equations are discussed briefly, and a method of dealing with certain non-linear equations is indicated. A description is also given of the propagation of errors in the fields due to various causes.

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