Open Access

ARTICLE

Efficient Numerical Scheme for Solving Large System of Nonlinear Equations

Mudassir Shams¹, Nasreen Kausar^2,*, Shams Forruque Ahmed³, Irfan Anjum Badruddin⁴, Syed Javed⁴

1 Department of Mathematics and Statistics, Riphah International University, I-14, Islamabad, 44000, Pakistan
2 Department of Mathematics, Yildiz Technical University, Faculty of Arts and Science, Esenler, 34210, Istanbul, Turkey
3 Science and Math Program, Asian University for Women, Chattogram, Bangladesh
4 Mechanical Engineering Department, College of Engineering, King Khalid University, Abha, 61421, Saudi Arabia

* Corresponding Author: Nasreen Kausar. Email:

Computers, Materials & Continua 2023, 74(3), 5331-5347. https://doi.org/10.32604/cmc.2023.033528

Received 19 June 2022; Accepted 15 September 2022; Issue published 28 December 2022

Abstract

A fifth-order family of an iterative method for solving systems of nonlinear equations and highly nonlinear boundary value problems has been developed in this paper. Convergence analysis demonstrates that the local order of convergence of the numerical method is five. The computer algebra system CAS-Maple, Mathematica, or MATLAB was the primary tool for dealing with difficult problems since it allows for the handling and manipulation of complex mathematical equations and other mathematical objects. Several numerical examples are provided to demonstrate the properties of the proposed rapidly convergent algorithms. A dynamic evaluation of the presented methods is also presented utilizing basins of attraction to analyze their convergence behavior. Aside from visualizing iterative processes, this methodology provides useful information on iterations, such as the number of diverging-converging points and the average number of iterations as a function of initial points. Solving numerous highly nonlinear boundary value problems and large nonlinear systems of equations of higher dimensions demonstrate the performance, efficiency, precision, and applicability of a newly presented technique.

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Keywords

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