Third and fourth order iterative methods free from second derivative for nonlinear systems

摘要

In this work, we develop a family of predictor–corrector methods free from second derivative for solving systems of nonlinear equations. In general, the obtained methods have order of convergence three but, in some particular cases the order is four. We also perform different numerical tests that confirm the theoretical results and allow us to compare these methods with Newton’s classical method and with other recently published methods.