IMPROVING THE ORDER OF A FIFTH-ORDER FAMILY OF VECTORIAL FIXED POINT SCHEMES BY INTRODUCING MEMORY

In this paper, we present a family of iterative schemes for solving nonlinear systems with 3 real parameters. If we do not fix values for the parameters this family has order 2, but if we fix two of them we obtain order 5. Starting from the fifth-order family, we study different ways of introducing memory, thus obtaining 6 order methods. We also analyze the efficiency indices of the family and of the methods with memory obtained from it, and we compare them with each other, as well as compare them with other known classes of iterative methods with order 5 and 6. Several numerical experiments are carried out to see the behaviour of the discussed methods, including dynamical planes to compare the stability of the different iterative schemes.