A family of fourth-order Steffensen-type methods with the applications on solving nonlinear ODEs (Q545958)

A family of fourth-order Steffensen-type two-step root-finders are proposed. Results of theoretical analysis and numerical experiments demonstrate that this family only uses three evaluations of the function per iteration to achieve the optimal fourth-order convergence for solving simple roots of nonlinear functions. The family also presents the opportunity to pursue iterative methods with better convergence than those of the typical second-order and third-order methods.