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.

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.

A family of fourth-order methods for solving non-linear equations

2007 ◽  
Vol 188 (1) ◽  
pp. 1031-1036 ◽  
Author(s):  
Jisheng Kou ◽  
Yitian Li ◽  
Xiuhua Wang
Keyword(s):  
Fourth Order ◽  
Linear Equations ◽  
Non Linear ◽  
Non Linear Equations

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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