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Computer Methodologies for the Comparison of Some Efficient Derivative Free Simultaneous Iterative Methods for Finding Roots of Non-Linear Equations

Yuming Chu1, Naila Rafiq2, Mudassir Shams3,*, Saima Akram4, Nazir Ahmad Mir3, Humaira Kalsoom5
1 Department of Mathematics, Huzhou University, Huzhou, 313000, China
2 Department of Mathematics, National University of Modern Languages, Islamabad, Pakistan
3 Department of Mathematics and Statistics, Riphah International University I-14, Islamabad, 44000, Pakistan
4 Center for Advanced Studies in Pure and Applied Mathematics Bahauddin Zakariya University, Multan, Pakistan
5 School of Mathematical Sciences, Zhejiang University, Hanghou, 310027, China
* Corresponding Author: Mudassir Shams. Email:

Computers, Materials & Continua 2021, 66(1), 275-290. https://doi.org/10.32604/cmc.2020.011907

Received 04 June 2020; Accepted 02 July 2020; Issue published 30 October 2020

Abstract

In this article, we construct the most powerful family of simultaneous iterative method with global convergence behavior among all the existing methods in literature for finding all roots of non-linear equations. Convergence analysis proved that the order of convergence of the family of derivative free simultaneous iterative method is nine. Our main aim is to check out the most regularly used simultaneous iterative methods for finding all roots of non-linear equations by studying their dynamical planes, numerical experiments and CPU time-methodology. Dynamical planes of iterative methods are drawn by using MATLAB for the comparison of global convergence properties of simultaneous iterative methods. Convergence behavior of the higher order simultaneous iterative methods are also illustrated by residual graph obtained from some numerical test examples. Numerical test examples, dynamical behavior and computational efficiency are provided to present the performance and dominant efficiency of the newly constructed derivative free family of simultaneous iterative method over existing higher order simultaneous methods in literature.

Keywords

Non-linear equation; iterative method; simultaneous method; basins of attractions; computational efficiency

Cite This Article

Y. Chu, N. Rafiq, M. Shams, S. Akram, N. Ahmad Mir et al., "Computer methodologies for the comparison of some efficient derivative free simultaneous iterative methods for finding roots of non-linear equations," Computers, Materials & Continua, vol. 66, no.1, pp. 275–290, 2021.

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This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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