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Computational Methods for Non-Linear Equations with Some Real-World Applications and Their Graphical Analysis

Amir Naseem1, M.A. Rehman1, Thabet Abdeljawad2,3,4,*

1 Department of Mathematics, University of Management and Technology, Lahore, Pakistan
2 Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia
3 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan
4 Department of Computer Science and Information Engineering, Asia University, Taichung, 41354, Taiwan

* Corresponding Author: Thabet Abdeljawad. Email: email

(This article belongs to this Special Issue: Recent Trends in Computational Methods for Differential Equations)

Intelligent Automation & Soft Computing 2021, 30(3), 805-819.


In this article, we propose some novel computational methods in the form of iteration schemes for computing the roots of non-linear scalar equations in a new way. The construction of these iteration schemes is purely based on exponential series expansion. The convergence criterion of the suggested schemes is also given and certified that the newly developed iteration schemes possess quartic convergence order. To analyze the suggested schemes numerically, several test examples have been given and then solved. These examples also include some real-world problems such as van der Wall’s equation, Plank’s radiation law and kinetic problem equation whose numerical results showing the better performance, applicability and efficiency of these iteration schemes against the other similar-nature two-step iteration schemes in the literature. Finally, a detailed graphical analysis of the suggested iteration schemes has been given in the form of polynomiographs for the different complex polynomials with the aid of computer technology that reveals the convergence characteristics and other dynamical features of the presented iteration schemes.


Cite This Article

A. Naseem, M. Rehman and T. Abdeljawad, "Computational methods for non-linear equations with some real-world applications and their graphical analysis," Intelligent Automation & Soft Computing, vol. 30, no.3, pp. 805–819, 2021.


cc 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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