Study of Dynamical Behavior and Stability of Iterative Methods for Nonlinear Equation with Applications in Engineering
Joint Authors
Akram, Saima
Rafiq, Naila
Mir, Nazir Ahmad
Shams, Mudassir
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-20, 20 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-07-27
Country of Publication
Egypt
No. of Pages
20
Main Subjects
Abstract EN
In this article, we first construct a family of optimal 2-step iterative methods for finding a single root of the nonlinear equation using the procedure of weight function.
We then extend these methods for determining all roots simultaneously.
Convergence analysis is presented for both cases to show that the order of convergence is 4 in case of the single-root finding method and is 6 for simultaneous determination of all distinct as well as multiple roots of a nonlinear equation.
The dynamical behavior is presented to analyze the stability of fixed and critical points of the rational operator of one-point iterative methods.
The computational cost, basins of attraction, efficiency, log of the residual, and numerical test examples show that the newly constructed methods are more efficient as compared with the existing methods in the literature.
American Psychological Association (APA)
Rafiq, Naila& Akram, Saima& Mir, Nazir Ahmad& Shams, Mudassir. 2020. Study of Dynamical Behavior and Stability of Iterative Methods for Nonlinear Equation with Applications in Engineering. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-20.
https://search.emarefa.net/detail/BIM-1194466
Modern Language Association (MLA)
Rafiq, Naila…[et al.]. Study of Dynamical Behavior and Stability of Iterative Methods for Nonlinear Equation with Applications in Engineering. Mathematical Problems in Engineering No. 2020 (2020), pp.1-20.
https://search.emarefa.net/detail/BIM-1194466
American Medical Association (AMA)
Rafiq, Naila& Akram, Saima& Mir, Nazir Ahmad& Shams, Mudassir. Study of Dynamical Behavior and Stability of Iterative Methods for Nonlinear Equation with Applications in Engineering. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-20.
https://search.emarefa.net/detail/BIM-1194466
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1194466