An efficient Steffensen-like iterative method with memory

Abstract

[EN] Some methods with memory for solving nonlinear equations are designed from known methods without memory. We increase the convergence order from 4 to 6 by using a free parameter accelerator by Newton's interpolatory polynomial of the third degree. So, its efficiency index is even better than optimal sixteenth-order methods without memory. Dynamical behavior on low-degree polynomials is analyzed, highly improving the stability properties of the original schemes. Numerical test problems are given to prove its competitiveness with methods of the same class.