Stability of different families of iterative methods with memory

Abstract

A family of derivative-free optimal iterative methods of order four, for solving nonlinear equations, is constructed by using weight function procedure. From its error equation, different iterative schemes with memory can be designed increasing the order of convergence up to six. The stability of the families, with and without memory, is studied in terms of the values of the parameters, in order to select the elements of the families with good properties of stability and avoid those that present chaotic behavior in the iterative process.