Two new three-step predictor-corrector methods with fifth-order convergence for solving nonlinear equations

In this paper, we present two new three-step predictor-corrector methods for solving nonlinear equations. This two algorithms are free from second derivative and per iteration they only require three evaluations of the given function and one evaluation of its first derivative. Convergence analysis shows that they are fifth-order convergent. Numerical tests demonstrate that both of the two new methods are more efficient and more practical than most of known variants of two-step methods.