A stable class of modified Newton-like methods for multiple roots and their dynamics
-
Munish Kansal
,
Alicia Cordero
Abstract
There have appeared in the literature a lot of optimal eighth-order iterative methods for approximating simple zeros of nonlinear functions. Although, the similar ideas can be extended for the case of multiple zeros but the main drawback is that the order of convergence and computational efficiency reduce dramatically. Therefore, in order to retain the accuracy and convergence order, several optimal and non-optimal modifications have been proposed in the literature. But, as far as we know, there are limited number of optimal eighth-order methods that can handle the case of multiple zeros. With this aim, a wide general class of optimal eighth-order methods for multiple zeros with known multiplicity is brought forward, which is based on weight function technique involving function-to-function ratio. An extensive convergence analysis is demonstrated to establish the eighth-order of the developed methods. The numerical experiments considered the superiority of the new methods for solving concrete variety of real life problems coming from different disciplines such as trajectory of an electron in the air gap between two parallel plates, the fractional conversion in a chemical reactor, continuous stirred tank reactor problem, Planck’s radiation law problem, which calculates the energy density within an isothermal blackbody and the problem arising from global carbon dioxide model in ocean chemistry, in comparison with methods of similar characteristics appeared in the literature.
Acknowledgments
This research was partially supported by PGC2018-095896-B-C22 (MCIU/AEI/FEDER, UE). The authors would like to thank the anonymous reviewers for their useful suggestions that have improved the final version of this manuscript.
Research funding: This research was partially supported by PGC2018-095896-B-C22 (MCIU/AEI/FEDER, UE).
Employment or leadership: None declared.
Honorarium: None declared.
Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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© 2020 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Original Research Articles
- Nonlinear Forced Vibration Analysis of FG Cylindrical Nanopanels Based on Mindlin’s Strain Gradient Theory and 3D Elasticity
- Numerical Solutions Based on a Collocation Method Combined with Euler Polynomials for Linear Fractional Differential Equations with Delay
- A Remanufacturing Duopoly Game Based on a Piecewise Nonlinear Map: Analysis and Investigations
- Development of a Momentum Transfer Coefficient in Particle Horizontal Channel Flow
- Analysis of a New Class of Impulsive Implicit Sequential Fractional Differential Equations
- On the Dynamics and Control of Fractional Chaotic Maps with Sine Terms
- A stable class of modified Newton-like methods for multiple roots and their dynamics
- Experimental and numerical studies on failure and energy absorption of composite thin-walled square tubes under quasi-static compression loading
- Existence of periodic solutions with minimal period for fourth-order discrete systems via variational methods
- Derivative free iterative methods with memory having higher R-order of convergence
Articles in the same Issue
- Frontmatter
- Original Research Articles
- Nonlinear Forced Vibration Analysis of FG Cylindrical Nanopanels Based on Mindlin’s Strain Gradient Theory and 3D Elasticity
- Numerical Solutions Based on a Collocation Method Combined with Euler Polynomials for Linear Fractional Differential Equations with Delay
- A Remanufacturing Duopoly Game Based on a Piecewise Nonlinear Map: Analysis and Investigations
- Development of a Momentum Transfer Coefficient in Particle Horizontal Channel Flow
- Analysis of a New Class of Impulsive Implicit Sequential Fractional Differential Equations
- On the Dynamics and Control of Fractional Chaotic Maps with Sine Terms
- A stable class of modified Newton-like methods for multiple roots and their dynamics
- Experimental and numerical studies on failure and energy absorption of composite thin-walled square tubes under quasi-static compression loading
- Existence of periodic solutions with minimal period for fourth-order discrete systems via variational methods
- Derivative free iterative methods with memory having higher R-order of convergence
