Efficient Numerical Scheme for Solving Large System of Nonlinear Equations

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Shams M., Kausar N., Ahmed S. F., Badruddin I. A., Javed S.

Computers, Materials and Continua, vol.74, no.3, pp.5331-5347, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 74 Issue: 3
  • Publication Date: 2023
  • Doi Number: 10.32604/cmc.2023.033528
  • Journal Name: Computers, Materials and Continua
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Compendex, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.5331-5347
  • Keywords: Nonlinear equations, convergence order, boundary value problem, computational time, basins of attraction, converging points
  • Yıldız Technical University Affiliated: Yes


© 2023 Tech Science Press. All rights reserved.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.