On developing an optimal Jarratt-like class for solving nonlinear equations

Abstract

It is attempted to derive an optimal class of methods without memory from Ozban’s method [A. Y. Ozban, Some New Variants of Newton’s Method, Appl. Math. Lett. 17 (2004) 677-682].  To this end, we try to introduce a weight function in the second step of the method and to find some suitable conditions, so that the modified method is optimal in the sense of Kung and Traub’s conjecture.  Also, convergence analysis along with numerical implementations are included to verify both theoretical and practical aspects of the proposed optimal class of methods without memory.