Unifying fourth-order family of iterative methods

Khattri, Sanjay Kumar; Noor, Muhammad Aslam; Al-Said, Eisa A.

doi:10.1016/j.aml.2011.02.009

Cited by 27 publications

(39 citation statements)

References 14 publications

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“…We employ the present methods [14], the method (WM) developed by Weerakoon et al [9], the method (OM) by Özban [16], the Jarratt method (JA) and the method (KA) developed by Khattri et al [18]. The computational order of convergence (COC) was given by (see [19]) x , the number of iterations N required to meet the stopping criteria, the value of ( ) 1 n f x + in the last iteration and the value of COC.…”

Section: Numerical Examplesmentioning

confidence: 99%

A Family of Combined Iterative Methods for Solving Nonlinear Equations

Chen¹,

Qian²

2017

AJAMS

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In this article we construct some higher-order modifications of Newton's method for solving nonlinear equations, which is based on the undetermined coefficients. This construction can be applied to any iteration formula. It can be found that per iteration the resulting methods add only one additional function evaluation, their order of convergence can be increased by two or three units. Higher order convergence of our methods is proved and corresponding asymptotic error constants are expressed. Numerical examples, obtained using Matlab with high precision arithmetic, are shown to demonstrate the convergence and efficiency of the combined iterative methods. It is found that the combined iterative methods produce very good results on tested examples, compared to the results produced by the existing higher order schemes in the related literature.

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Section: Numerical Examplesmentioning

confidence: 99%

A Family of Combined Iterative Methods for Solving Nonlinear Equations

Chen¹,

Qian²

2017

AJAMS

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“…Khattri et al [1] suggested three cases (i) α = 6, β = −1, η = 2.5, m = 2, (ii) α = 5.5, β = 1, η = 2.5, m = 2, and (iii) α = 2, β = 1, η = 2.5, m = 1 of their proposed family. Here, we consider these cases and call them KB1, KB2, and KB3, respectively.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…In the next section we plot the basins of attraction for these cases along with the basins for several members of King's family of methods and the cases presented in [1] to find the best performer.…”

Section: Extraneous Fixed Pointsmentioning

confidence: 99%

“…Wang and Liu [11] and Thukral and Petković [12] have developed optimal eighth order methods. Khattri and Babajee [1] has developed the following optimal fourth order 3 parameter family of methods…”

Section: Introductionmentioning

confidence: 99%

“…

In this paper we analyze an optimal fourth-order family of methods suggested by Khattri and Babajee, (2013). We analyze the family using the information on the extraneous fixed points.

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confidence: 99%

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