New seventh and eighth order derivative free methods for solving nonlinear equations

Panday, Bhavna; Jaiswal, J. P.

doi:10.1515/tmj-2017-0049

Cited by 2 publications

(1 citation statement)

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“…Applications to diverse problems and comparisons with established methods are conducted to assess their effectiveness. [16] suggests two innovative iterative methods for solving nonlinear equations, demonstrating seventh and eighth-order convergence and requiring only four function evaluations per iteration, aligning with the Kung-Traub conjecture on optimal order for schemes without memory. Moreover, [26] presents three iterative methods of orders three, six, and seven for solving nonlinear equations.…”

Section: Introductionmentioning

confidence: 85%

A three step seventh order iterative method for solution nonlinear equation using Lagrange interpolation technique

Jamali,

Lakho,

Kalhoro

et al. 2024

VFAST trans. math.

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This research paper comprehensively presents the derivation of a seventh-order iteration scheme designed to obtain simple roots of nonlinear equations through the utilization of Lagrange interpolation technique. The scheme is characterized by the requirement for three function evaluations and one evaluation of the first derivative in each iteration. A detailed convergence analysis is also carried out to assess the efficacy of the proposed method. Additionally, the paper includes comprehensive numerical experiments aimed at confirming the theoretical results and illustrating the competitive performance of the derived iteration scheme.

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Section: Introductionmentioning

confidence: 85%