Designing new derivative-free memory methods to solve nonlinear scalar problems

Abstract

In this work, two families of iterative methods without derivatives have been designed using the composition of iterative schemes and the inclusion of weight functions. The convergence analysis of the two-step and the three-step families is presented, showing the necessary conditions that must be satisfied by the weight functions to have order four and six, respectively. From them, two methods with memory have been derived, improving their order of convergence and their efficiency. All the methods are tested and compared with other known methods in the approxitation of the roots of different nonlinear functions. The results show the improvement of the classes after including memory.