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On iterative techniques for estimating all roots of nonlinear equation and its system with application in differential equation

Authors
  • Shams, Mudassir1
  • Rafiq, Naila2
  • Kausar, Nasreen3
  • Agarwal, Praveen4, 5, 6
  • Park, Choonkil7
  • Mir, Nazir Ahmad1, 2
  • 1 Riphah International University I-14, Islamabad, 44000, Pakistan , Islamabad (Pakistan)
  • 2 NUML, Islamabad, Pakistan , Islamabad (Pakistan)
  • 3 Yildiz Technical University, Esenler, Istanbul, 34210, Turkey , Istanbul (Turkey)
  • 4 Anand International College of Engineering, Jaipur, Rajasthan, 303012, India , Jaipur (India)
  • 5 Harish-Chandra Research Institute, Allahabad, 211019, India , Allahabad (India)
  • 6 International Center for Basic and Applied Sciences, Jaipur, 302029, India , Jaipur (India)
  • 7 Hanyang University, Seoul, South Korea , Seoul (South Korea)
Type
Published Article
Journal
Advances in Difference Equations
Publisher
Springer International Publishing
Publication Date
Nov 05, 2021
Volume
2021
Issue
1
Identifiers
DOI: 10.1186/s13662-021-03636-x
Source
Springer Nature
Keywords
Disciplines
  • Difference Equations, Special Functions and Orthogonal Polynomials
License
Green

Abstract

In this article, we construct a family of iterative methods for finding a single root of nonlinear equation and then generalize this family of iterative methods for determining all roots of nonlinear equations simultaneously. Further we extend this family of root estimating methods for solving a system of nonlinear equations. Convergence analysis shows that the order of convergence is 3 in case of the single root finding method as well as for the system of nonlinear equations and is 5 for simultaneous determination of all distinct and multiple roots of a nonlinear equation. The computational cost, basin of attraction, efficiency, log of residual and numerical test examples show that the newly constructed methods are more efficient as compared to the existing methods in literature.

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