Open Access

ARTICLE

Computer Geometries for Finding All Real Zeros of Polynomial Equations Simultaneously

Naila Rafiq¹, Saima Akram², Mudassir Shams^3,*, Nazir Ahmad Mir¹

1 Department of Mathematics, NUML, Islamabad, 44000, Pakistan
2 Centre for Advanced Studies in Pure & Applied Mathematics, Bahauddin Zakariya University, Multan
3 Department of Mathematics and Statistics, Riphah International University I-14, Islamabad, 44000, Pakistan

* Corresponding Author: Mudassir Shams. Email:

(This article belongs to the Special Issue: Role of Computer in Modelling & Solving Real-World Problems)

Computers, Materials & Continua 2021, 69(2), 2635-2651. https://doi.org/10.32604/cmc.2021.018955

Received 26 March 2021; Accepted 27 April 2021; Issue published 21 July 2021

Abstract

In this research article, we construct a family of derivative free simultaneous numerical schemes to approximate all real zero of non-linear polynomial equation. We make a comparative analysis of the newly constructed numerical schemes with a well-known existing simultaneous method for determining all the distinct real zeros of polynomial equations using computer algebra system Mat Lab. Lower bound of convergence of simultaneous schemes is calculated using Mathematica. Global convergence property of the numerical schemes is presented by taking random starting initial approximation and their convergence history are graphically presented. Some real life engineering applications along with some higher degree polynomials are considered as numerical test problems to show performance and efficiency of the derivative free family of numerical methods with comparison of an existing method of same order in literature. Local computational order of convergence, CPU time, graph of computational order of convergence and residual error graphs elaborate efficiency, robustness and authentication of the suggested family of numerical methods in its domain.

---

Keywords

---