Construction of Iterative Adaptive Methods with Memory with 100% Improvement of Convergence Order

An effcient family of the recursive methods of adaptive is proposed for solving nonlinear equations and is developed such that all previous information is applied. These methods have reached the max- imum degree of convergence improvement of 100% and also have an effciency index of 2. Three families have been examined from Steffensen- Like single, two, and three-step methods that have used 2, 3 and 4 pa- rameters, respectively. Numerical comparisons have made with other ex- isting methods one-, two-, three-, and four-point to show the performance of the convergence speed of the proposed method and conrm theoret- ical results.