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ARTICLE
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
Cite This Article
APA Style
Chu, Y., Rafiq, N., Shams, M., Akram, S., Mir, N.A. et al. (2021). Computer methodologies for the comparison of some efficient derivative free simultaneous iterative methods for finding roots of non-linear equations. Computers, Materials & Continua, 66(1), 275-290. https://doi.org/10.32604/cmc.2020.011907
Vancouver Style
Chu Y, Rafiq N, Shams M, Akram S, Mir NA, Kalsoom H. Computer methodologies for the comparison of some efficient derivative free simultaneous iterative methods for finding roots of non-linear equations. Comput Mater Contin. 2021;66(1):275-290 https://doi.org/10.32604/cmc.2020.011907
IEEE Style
Y. Chu, N. Rafiq, M. Shams, S. Akram, N.A. Mir, and H. Kalsoom "Computer Methodologies for the Comparison of Some Efficient Derivative Free Simultaneous Iterative Methods for Finding Roots of Non-Linear Equations," Comput. Mater. Contin., vol. 66, no. 1, pp. 275-290. 2021. https://doi.org/10.32604/cmc.2020.011907
Citations