On the improvement of the order of convergence of iterative methods for solving nonlinear systems by means of memory

Abstract

Iterative methods with memory for solving nonlinear systems have been designed. For approximating the accelerating parameters the Kurchatov's divided difference is used as an approximation of the derivative of second order. The convergence of the proposed schemes is analyzed by means of Taylor expansions. Numerical examples are shown to compare the performance of the proposed schemes with other known ones, confirming the theoretical results.