In this paper, we present six new fourth-order methods with closed formulae for finding multiple roots of nonlinear equations. The first four of them require one-function and three-derivative evaluation per iteration. The last two require one-function and two-derivative evaluation per iteration. Several numerical examples are given to show the performance of the presented methods compared with some known methods.
Li, S. G., Cheng, L. Z., & Neta, B. (2010). Some fourth-order nonlinear solvers with closed formulae for multiple roots. Computers and Mathematics with Applications, 59(1), 126–135. https://doi.org/10.1016/j.camwa.2009.08.066