Abstract. In this paper, we present a two parameter modified families of Jarratt's method having quartic convergence for computing simple roots of nonlinear equations, permitting f'(x)=0 in the vicinity of the required root. The present approach of deriving this optimal class of Jarratt's method is based on applying weight function approach. Jarratt's method and Zhou et al. family of methods [#!Zhou!#] for simple roots can be seen as special cases of our proposed scheme. Each member of the class requires three functional evaluations per iteration. The performance of proposed multipoint methods is compared with its closest competitors namely, King's method, Ostrowski's method and Jarratt's method in a series of numerical experiments. All the methods considered here are found to be more effective and comparable to the similar robust methods available in the literature.

Received: October 26, 2012

AMS Subject Classification: 65xx, 65Hxx

Key Words and Phrases: nonlinear equations, simple roots, Newton's method, Jarratt's method, optimal order of convergence, efficiency index

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