Ball comparison for three optimal eight order methods under weak conditions

Ioannis K. Argyros, Santhosh George

Abstract


We considered three optimal eighth order method for solving nonlinear equations. In earlier studies Taylors expansions and  hypotheses reaching up to the eighth derivative are used to prove the convergence of these methods. These hypotheses restrict the applicability of the methods. In our study we use  hypotheses on the first derivative. Numerical examples  illustrating the theoretical results are also presented in this study.

Keywords


Banach space; Fr\'{e}chet derivative; Efficiency index; ball convergence.

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References


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DOI: http://dx.doi.org/10.24193/subbmath.2019.3.12

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