Another sixth-order iterative method free from derivative for solving multiple roots of a nonlinear equation

Qudsi, Rahma; Imran, M.; Syamsudhuha,

doi:10.12988/ams.2017.76208

Cited by 3 publications

(2 citation statements)

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“…For numerous zeros of nonlinear functions, various authors recently devised optimal and non-optimal (in terms of the Kung-Traub hypothesis; see [2]) non-derivative approaches [3][4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Efficient Fourth-Order Scheme for Multiple Zeros: Applications and Convergence Analysis in Real-Life and Academic Problems

Kumar,

Behl,

Alrajhi

2023

Mathematics

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High-order iterative techniques without derivatives for multiple roots have wide-ranging applications in the following: optimization tasks, where the objective function lacks explicit derivatives or is computationally expensive to evaluate; engineering; design finance; data science; and computational physics. The versatility and robustness of derivative-free fourth-order methods make them a valuable tool for tackling complex real-world optimization challenges. An optimal extension of the Traub–Steffensen technique for finding multiple roots is presented in this work. In contrast to past studies, the new expanded technique effectively handles functions with multiple zeros. In addition, a theorem is presented to analyze the convergence order of the proposed technique. We also examine the convergence analysis for four real-life problems, namely, Planck’s law radiation, Van der Waals, the Manning equation for isentropic supersonic flow, the blood rheology model, and two well-known academic problems. The efficiency of the approach and its convergence behavior are studied, providing valuable insights for practical and academic applications.

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Section: Introductionmentioning

confidence: 99%

Efficient Fourth-Order Scheme for Multiple Zeros: Applications and Convergence Analysis in Real-Life and Academic Problems

Kumar,

Behl,

Alrajhi

2023

Mathematics

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“…Sharma et al [17], Kumar et al [9,10], Behl et al [2] and Rani and Kansal [13] proposed a fourth-order root finding methods for multiple roots. Qudsi et al [11,12] presented three step sixth order iterative methods for finding the multiple roots. Sharma et al [15] proposed seventh order convergent iterative scheme for multiple roots.…”

Section: Introductionmentioning

confidence: 99%

An optimal eighth order derivative free multiple root finding numerical method and applications to chemistry

et al. 2022

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In this paper, we present an optimal eighth order derivative-free family of methods for multiple roots which is based on the first order divided difference and weight functions. This iterative method is a three step method with the first step as Traub–Steffensen iteration and the next two taken as Traub–Steffensen-like iteration with four functional evaluations per iteration. We compare our proposed method with the recent derivative-free methods using some chemical engineering problems modelled as nonlinear equations with simple and multiple roots. Stability of the presented family of methods is demonstrated by using the graphical tool known as basins of attraction.

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New Higher Order Iterative Method for Multiple Roots of Nonlinear Equations

Panday

Chanu

Devi

2023

Springer Proceedings in Mathematics &Amp; Statistics

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Another sixth-order iterative method free from derivative for solving multiple roots of a nonlinear equation

Cited by 3 publications

References 0 publications

Efficient Fourth-Order Scheme for Multiple Zeros: Applications and Convergence Analysis in Real-Life and Academic Problems

Efficient Fourth-Order Scheme for Multiple Zeros: Applications and Convergence Analysis in Real-Life and Academic Problems

An optimal eighth order derivative free multiple root finding numerical method and applications to chemistry

New Higher Order Iterative Method for Multiple Roots of Nonlinear Equations

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