Derivative free iterative methods with memory having higher R-order of convergence
-
Pankaj Jain
and
Prem Bahadur Chand
Abstract
We derive two iterative methods with memory for approximating a simple root of any nonlinear equation. For this purpose, we take two optimal methods without memory of order four and eight and convert them into the methods with memory without increasing any further function evaluation. These methods involve a self-accelerator (parameter) that depends upon the iteration index to increase the order of the optimal methods. Consequently, the efficiency of the new methods is considerably high as compared to the methods without memory. Some numerical examples are provided in support of the theoretical results.
Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: None declared.
Employment or leadership: None declared.
Honorarium: None declared.
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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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
