Research Article

The basins of attraction for optimal fourth-eighth order methods

Abstract: We developed a completely new, eighth- and fourth-order optimal approach for solving nonlinear equations in this study. With three function evaluations, the new methods’ convergence order is four; with four function evaluations, it is eight. Furthermore, according to the Kung-Traub hypothesis, it is optimal. In order to illustrate their dynamic behaviour on the complex plane, the basins of attraction are provided.