Design of iterative methods with memory for solving nonlinear systems

In this paper, we design two parametric classes of iterative methods without memory to solve nonlinear systems, whose convergence order is 4 and 7, respectively. From their error equations and to increase the convergence order without performing new functional evaluations, memory is introduced in these families of different forms. That allows us to increase from 4 to 6 the convergence order in the first family and from 7 to 11 in the second one. We perform some numerical experiments with big size systems for confirming the theoretical results and comparing the proposed methods along other known schemes.