A Steffensen type optimal eighth order multiple root finding scheme for nonlinear equations

Abstract

In this study, we introduce a novel weight function-based eighth order derivative-free method for locating repeated roots of nonlinear equations. It is a three-step Steffensen-type scheme with first order divided differences in place of the first order derivatives. It is noteworthy that so far only few eighth order derivative free multiple root finding scheme exist in literature. Different nonlinear standard and applications based nonlinear functions are used to demonstrate the applicability of the suggested approach and to confirm its strong convergence tendency. Drawing basins of attraction on the graphical regions demonstrates how the offered family of approaches converge.