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We have given two general methods of converting with derivative two-step methods to without derivative two-step methods. It can also be observed that this conversion not only retain the optimal order of convergence of the two-step methods but the resulting derivative free families of iterative methods are also extendable to with memory class. The with-memory methods show greater acceleration in the order of convergence. In this way, order of convergence is accelerated from 4 to 7.53 at the most. An extensive comparison of our methods is done with the recent methods of respective domain. c ©2016 All rights reserved.

Construction of Tri-parametric derivative free fourth order with and without memory iterative method