Revisit of Jarratt method for solving nonlinear equations

Authors:
Fazlollah Soleymani
Affiliations:
Department of Mathematics, Young Researchers Club, Zahedan Branch, Islamic Azad University, Zahedan, Iran
Venue:
Numerical Algorithms
Year:
2011

Citing 3
Cited 2

Optimal Order of One-Point and Multipoint Iteration

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On a General Class of Multipoint Root-Finding Methods of High Computational Efficiency

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Semilocal convergence of a multipoint fourth-order super-Halley method in Banach spaces

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Regarding the accuracy of optimal eighth-order methods

Mathematical and Computer Modelling: An International Journal
An efficient twelfth-order iterative method for finding all the solutions of nonlinear equations

Journal of Computational Methods in Sciences and Engineering

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Abstract

In this paper, some sixth-order modifications of Jarratt method for solving single variable nonlinear equations are proposed. Per iteration, they consist of two function and two first derivative evaluations. The convergence analyses of the presented iterative methods are provided theoretically and a comparison with other existing famous iterative methods of different orders is given. Numerical examples include some of the newest and the most efficient optimal eighth-order schemes, such as Petkovic (SIAM J Numer Anal 47:4402---4414, 2010), to put on show the accuracy of the novel methods. Finally, it is also observed that the convergence radii of our schemes are better than the convergence radii of the optimal eighth-order methods.