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

Mudassir Shams1,*, Naila Rafiq2, Nazir Ahmad Mir1,2, Babar Ahmad3, Saqib Abbasi1, Mutee-Ur-Rehman Kayani1
1 Department of Mathematics and Statistics, Riphah International University, I-14, Islamabad, 44000, Pakistan
2 Department of Mathematics, NUML, Islamabad, Pakistan
3 Department of Mathematics, Comsats University, Islamabad, 44000, Pakistan
* Corresponding Author: Mudassir Shams. Email:

Computer Systems Science and Engineering 2021, 36(3), 493-507.

Received 22 September 2020; Accepted 24 November 2020; Issue published 18 January 2021


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.


Non-linear equation; inverse iterative method; simultaneous method; basins of attraction; lower bound of convergence

Cite This Article

M. Shams, N. Rafiq, N. Ahmad Mir, B. Ahmad, S. Abbasi et al., "On computer implementation for comparison of inverse numerical schemes for non-linear equations," Computer Systems Science and Engineering, vol. 36, no.3, pp. 493–507, 2021.

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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