Analysis of optimal iterative methods from a dynamical point of view by studying their stability properties

Kansal, Munish; Sharma, Himani

doi:10.1007/s10910-023-01523-2

Cited by 2 publications

(1 citation statement)

References 12 publications

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“…It has been observed that iterative schemes stable for such functions tend to perform better when applied to more complicated functions than methods exhibiting pathologies. To this end, the tools of complex discrete dynamics are employed to analyze stability in quadratic polynomials (see for example the work of Amat et al in [13,14], Argyros et al in [15], Behl et al in [16], Chicharro et al in [17], Rafiq et al in [18], Kansal et al in [19], Khirallah et al in [20], and Moccari et al in [21], among others).…”

Section: Introduction and Preliminary Conceptsmentioning

confidence: 99%

Stability Analysis of a New Fourth-Order Optimal Iterative Scheme for Nonlinear Equations

Cordero,

Reyes,

Torregrosa

et al. 2023

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In this paper, a new parametric class of optimal fourth-order iterative methods to estimate the solutions of nonlinear equations is presented. After the convergence analysis, a study of the stability of this class is made using the tools of complex discrete dynamics, allowing those elements of the class with lower dependence on initial estimations to be selected in order to find a very stable subfamily. Numerical tests indicate that the stable members perform better on quadratic polynomials than the unstable ones when applied to other non-polynomial functions. Moreover, the performance of the best elements of the family are compared with known methods, showing robust and stable behaviour.

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Section: Introduction and Preliminary Conceptsmentioning

confidence: 99%

Stability Analysis of a New Fourth-Order Optimal Iterative Scheme for Nonlinear Equations

Cordero,

Reyes,

Torregrosa

et al. 2023

Axioms

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Design and dynamical behavior of a fourth order family of iterative methods for solving nonlinear equations

Cordero,

Ledesma,

Maimó

et al. 2024

MATH

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<abstract><p>In this paper, a new fourth-order family of iterative schemes for solving nonlinear equations has been proposed. This class is parameter-dependent and its numerical performance depends on the value of this free parameter. For studying the stability of this class, the rational function resulting from applying the iterative expression to a low degree polynomial was analyzed. The dynamics of this rational function allowed us to better understand the performance of the iterative methods of the class. In addition, the critical points have been calculated and the parameter spaces and dynamical planes have been presented, in order to determine the regions with stable and unstable behavior. Finally, some parameter values within and outside the stability region were chosen. The performance of these methods in the numerical section have confirmed not only the theoretical order of convergence, but also their stability. Therefore, the robustness and wideness of the attraction basins have been deduced from these numerical tests, as well as comparisons with other existing methods of the same order of convergence.</p></abstract>

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Analysis of optimal iterative methods from a dynamical point of view by studying their stability properties

Cited by 2 publications

References 12 publications

Stability Analysis of a New Fourth-Order Optimal Iterative Scheme for Nonlinear Equations

Stability Analysis of a New Fourth-Order Optimal Iterative Scheme for Nonlinear Equations

Design and dynamical behavior of a fourth order family of iterative methods for solving nonlinear equations

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