Inverse Family of Numerical Methods for Approximating All Simple and Roots with Multiplicity of Nonlinear Polynomial Equations with Engineering Applications

Author:

Shams Mudassir1ORCID,Rafiq Naila2ORCID,Kausar Nasreen3ORCID,Ahmed Shams Forruque4ORCID,Mir Nazir Ahmad2ORCID,Chandra Saha Suvash5ORCID

Affiliation:

1. Department of Mathematics and Statistics, Riphah International University I-14, Islamabad 44 000, Pakistan

2. Department of Mathematics, National University of Modern Languages, Islamabad, Pakistan

3. Deperament of Mathematics, Yildiz Technical University, Faculty of Arts and Science, Esenler 34 210, Istanbul, Turkey

4. Science and Math Program, Asian University for Women, Chattogram 4000, Bangladesh

5. School of Mechanical and Mechatronic Engineering University of Technology Sydney (UTS), Sydney, Australia

Abstract

A new inverse family of the iterative method is interrogated in the present article for simultaneously estimating all distinct and multiple roots of nonlinear polynomial equations. Convergence analysis proves that the order of convergence of the newly constructed family of methods is two. The computer algebra systems CAS-Mathematica is used to determine the lower bound of convergence order, which justifies the local convergence of the newly developed method. Some nonlinear models from physics, chemistry, and engineering sciences are considered to demonstrate the performance and efficiency of the newly constructed family of inverse simultaneous methods in comparison to classical methods in the literature. The computational time in seconds and residual error graph of the inverse simultaneous methods are also presented to elaborate their convergence behavior.

Publisher

Hindawi Limited

Subject

General Engineering,General Mathematics

Reference22 articles.

1. On highly efficient derivative-free family of numerical methods for solving polynomial equation simultaneously;M. Shams;Advances in Difference Equations,2021

2. Stability and applicability of iterative methods with memory

3. Generating root-finder iterative methods of second order convergence and stability,axioms;F. I. Chicharro,2019

4. Some variants of Halley’s method with memory and their applications for solving several chemical problems

5. Computer methodologies for the comparison of some efficient derivative free simultaneous iterative methods for finding roots of non-linear equations;Y. M. Chu,2020

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