On Computer Implementation for Comparison of Inverse Numerical Schemes for Non-Linear Equations

Shams,, Mudassir and Rafiq, Naila and Mir, Nazir Ahmad and Ahmad, Babar and Abbasi, Saqib and Kayani, Mutee-Ur-Rehman (2021) On Computer Implementation for Comparison of Inverse Numerical Schemes for Non-Linear Equations. Computer Systems Science & Engineering, 2021 (36). pp. 493-507. ISSN 0267-6192

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Abstract

In this research article, we interrogate two new modifications in inverse
Weierstrass iterative method for estimating all roots of non-linear equation simultaneously.
These modifications enables us to accelerate the convergence order of
inverse Weierstrass method from 2 to 3. Convergence analysis proves that the
orders of convergence of the two newly constructed inverse methods are 3. Using
computer algebra system Mathematica, we find the lower bound of the convergence
order and verify it theoretically. Dynamical planes of the inverse simultaneous
methods and classical iterative methods are generated using MATLAB
(R2011b), to present the global convergence properties of inverse simultaneous
iterative methods as compared to classical methods. Some non-linear models
are taken from Physics, Chemistry and engineering to demonstrate the performance
and efficiency of the newly constructed methods. Computational CPU
time, and residual graphs of the methods are provided to present the dominance
behavior of our newly constructed methods as compared to existing inverse
and classical simultaneous iterative methods in the literature.

Item Type:	Article
Uncontrolled Keywords:	Non-linear equation; inverse iterative method; simultaneous method; basins of attraction; lower bound of convergence
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/1292

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