New derivative-free iterative family having optimal convergence order sixteen and its applications

PurposeThe purpose of the article is to construct a new class of higher-order iterative techniques for solving scalar nonlinear problems.Design/methodology/approachThe scheme is generalized by using the power-mean notion. By applying Neville's interpolating technique, the methods are formulated...

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Bibliographic Details
Published in:Engineering computations Vol. 39; no. 3; pp. 965 - 992
Main Authors: Kaur, Manpreet, Kumar, Sanjeev, Kansal, Munish
Format: Journal Article
Language:English
Published: Bradford Emerald Publishing Limited 04.03.2022
Emerald Group Publishing Limited
Subjects:
Approximation
Chemical reactors
Convergence
Efficiency
Eigenvalues
Iterative methods
Methods
Nonlinear equations
Power
Workloads
Chemical equilibrium
With and without memory methods
65Y20
Iterative methods
Basins of attraction
65H05
Kung-Traub conjecture
ISSN:0264-4401, 1758-7077
Online Access:Get full text
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Summary:PurposeThe purpose of the article is to construct a new class of higher-order iterative techniques for solving scalar nonlinear problems.Design/methodology/approachThe scheme is generalized by using the power-mean notion. By applying Neville's interpolating technique, the methods are formulated into the derivative-free approaches. Further, to enhance the computational efficiency, the developed iterative methods have been extended to the methods with memory, with the aid of the self-accelerating parameter.FindingsIt is found that the presented family is optimal in terms of Kung and Traub conjecture as it evaluates only five functions in each iteration and attains convergence order sixteen. The proposed family is examined on some practical problems by modeling into nonlinear equations, such as chemical equilibrium problems, beam positioning problems, eigenvalue problems and fractional conversion in a chemical reactor. The obtained results confirm that the developed scheme works more adequately as compared to the existing methods from the literature. Furthermore, the basins of attraction of the different methods have been included to check the convergence in the complex plane.Originality/valueThe presented experiments show that the developed schemes are of great benefit to implement on real-life problems.
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ISSN:0264-4401
1758-7077
DOI:10.1108/EC-03-2021-0155