Modified Bisection Algorithm for Multiple Roots of Nonlinear Equation With the R Software

2019 ◽  
Author(s):  
Mohammed Ridha Kouider
Keyword(s):  
Nonlinear Equation ◽  
Multiple Roots ◽  
R Software ◽  
Bisection Algorithm

scholarly journals Fifth-Order Iterative Method for Solving Multiple Roots of the Highest Multiplicity of Nonlinear Equation

Algorithms ◽  
2015 ◽  
Vol 8 (3) ◽  
pp. 656-668 ◽  
Author(s):  
Juan Liang ◽  
Xiaowu Li ◽  
Zhinan Wu ◽  
Mingsheng Zhang ◽  
Lin Wang ◽  
...  
Keyword(s):  
Nonlinear Equation ◽  
Iterative Method ◽  
Multiple Roots ◽  
Fifth Order

scholarly journals On Dynamics of Iterative Techniques for Nonlinear Equation with Applications in Engineering

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Mudassir Shams ◽  
Nazir Ahmad Mir ◽  
Naila Rafiq ◽  
A. Othman Almatroud ◽  
Saima Akram
Keyword(s):  
Nonlinear Equation ◽  
Numerical Test ◽  
Computational Cost ◽  
Basins Of Attraction ◽  
Optimal Order ◽  
Multiple Roots ◽  
Optimal Order Of Convergence ◽  
Single Root ◽  
Root Finding

In this article, we construct an optimal family of iterative methods for finding the single root and then extend this family for determining all the distinct as well as multiple roots of single-variable nonlinear equations simultaneously. Convergence analysis is presented for both the cases to show that the optimal order of convergence is 4 in the case of single root finding methods and 6 for simultaneous determination of all distinct as well as multiple roots of a nonlinear equation. The computational cost, basins of attraction, efficiency, log of residual, and numerical test examples show that the newly constructed methods are more efficient as compared to the existing methods in the literature.

scholarly journals An Optimal Derivative Free Family of Chebyshev–Halley’s Method for Multiple Zeros

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 546
Author(s):  
Ramandeep Behl ◽  
Sonia Bhalla ◽  
Ángel Alberto Magreñán ◽  
Alejandro Moysi
Keyword(s):  
Nonlinear Equation ◽  
Weight Function ◽  
Convergence Analysis ◽  
Nonlinear Equations ◽  
Fourth Order ◽  
Order Of Convergence ◽  
Higher Order ◽  
Multiple Roots ◽  
Iterative Technique ◽  
Derivative Free

In this manuscript, we introduce the higher-order optimal derivative-free family of Chebyshev–Halley’s iterative technique to solve the nonlinear equation having the multiple roots. The designed scheme makes use of the weight function and one parameter α to achieve the fourth-order of convergence. Initially, the convergence analysis is performed for particular values of multiple roots. Afterward, it concludes in general. Moreover, the effectiveness of the presented methods are certified on some applications of nonlinear equations and compared with the earlier derivative and derivative-free schemes. The obtained results depict better performance than the existing methods.

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