A variant of Steffensen–King’s type family with accelerated sixth-order convergence and high efficiency index: Dynamic study and approach

Lotfi, Taher; Magreñán, Á. Alberto; Mahdiani, Katayoun; Rainer, J. Javier

doi:10.1016/j.amc.2014.12.033

Cited by 15 publications

(5 citation statements)

References 18 publications

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“…This will be checked in the numerical section of this manuscript. This is a standard procedure used in last years for many authors in this area of research (see, for example [2,5,15,16,17]).…”

Section: Dynamical Analysis Of Methods Without Memorymentioning

confidence: 99%

Widening basins of attraction of optimal iterative methods

et al. 2016

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In this work, we analyze the dynamical behavior on quadratic polynomials of a class of derivativefree optimal parametric iterative methods, designed by Khattri and Steihaug. By using their parameter as an accelerator, we develop different methods with memory of orders three, six and twelve, without adding new functional evaluations. Then a dynamical approach is made, comparing each of the proposed methods with the original ones without memory, with the following empiric conclusion: basins of attraction of iterative schemes with memory are wider and the behavior is more stable. This has been numerically checked by estimating the solution of a practical problem, as the friction factor of a pipe and also of other nonlinear academic problems.

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Section: Dynamical Analysis Of Methods Without Memorymentioning

confidence: 99%

Widening basins of attraction of optimal iterative methods

et al. 2016

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“…Cord2,Cord,Cordb,Cord1,CT,DH,DP,HRE,J,LMMR,QJPL,PC,QJF,P [5,6,7,10,9,11,12,15,17,20,22,21,23,26,30].…”

Section: Arg3mentioning

confidence: 99%

A Steffensen type method of two steps in Banach spaces with applications

Amat

Busquier

Ezquerro

et al. 2016

Journal of Computational and Applied Mathematics

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Please cite this article as: S. Amat, S. Busquier, J.A. Ezquerro, M.A. Hernández-Verón, A Steffensen type method of two steps in Banach spaces with applications, Journal of Computational and Applied Mathematics (2015), http://dx. AbstractThis paper is devoted to the analysis of a Steffensen-type of two steps with order of convergence at least three. The main advantage of this method is that it does not need to evaluate any Fréchet derivative or any bilinear operator. The method includes extra parameters in the divided difference in order to ensure a good approximation to the first derivative in each iteration. We prove, using recurrence relations, a semilocal convergence result in Banach spaces and do a detailed study of the domain of parameters associated to this result. Finally, some numerical results, including differentiable and nondifferentiable operators, are presented. Special attention is paid in the approximation of solutions of boundary problems using the multiple shooting method and in the approximation of a nonlinear model related with image processing.

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“…In this section, we will show some dynamical planes, as it appears in different studies such as [25][26][27][28][29][30], associated with the families (48) and (49), but applied to the polynomial p(z) = (z − 1) 2 (z + 1) with a double root z = 1 and a simple one z = −1 for different values of α and γ.…”

Section: Dynamical Planes Of (48) and (49)mentioning

confidence: 99%

An Optimal Derivative Free Family of Chebyshev–Halley’s Method for Multiple Zeros

et al. 2021

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In this manuscript, we introduce the higher-order optimal derivative-free family of Chebyshev–Halley’s iterative technique to solve the nonlinear equation having the multiple roots. The designed scheme makes use of the weight function and one parameter α to achieve the fourth-order of convergence. Initially, the convergence analysis is performed for particular values of multiple roots. Afterward, it concludes in general. Moreover, the effectiveness of the presented methods are certified on some applications of nonlinear equations and compared with the earlier derivative and derivative-free schemes. The obtained results depict better performance than the existing methods.

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A variant of Steffensen–King’s type family with accelerated sixth-order convergence and high efficiency index: Dynamic study and approach

Cited by 15 publications

References 18 publications

Widening basins of attraction of optimal iterative methods

Widening basins of attraction of optimal iterative methods

A Steffensen type method of two steps in Banach spaces with applications

An Optimal Derivative Free Family of Chebyshev–Halley’s Method for Multiple Zeros

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