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

Chu, Yuming and Rafiq, Naila and Shams, Mudassir and Akram4, Saima and Mir, Nazir Ahmad and Kalsoom, Humaira (2020) 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). pp. 275-290. ISSN 1546-2226;1546-2218

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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.

Item Type: Article
Uncontrolled Keywords: Non-linear equation; iterative method; simultaneous method; basins of attractions; computational efficiency
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Engineering and Applied Sciences (FEAS) > Department of Basic Sciences Islamabad
Depositing User: Mr Mudassir Shams
Date Deposited: 05 Apr 2021 09:19
Last Modified: 05 Apr 2021 09:19
URI: http://research.riphah.edu.pk/id/eprint/1291

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