Modified Chebyshev‐Halley type method and its variants for computing multiple roots

We present two families of third order methods for finding multiple roots of nonlinear equations. One family is based on the Chebyshev‐Halley scheme (for simple roots) and includes Halley, Chebyshev and Chun‐Neta methods as particular cases for multiple roots. The second family is based on the variant of Chebyshev‐Halley scheme and includes the methods of Dong, Homeier, Neta and Li et al. as particular cases. The efficacy is tested on a number of relevant numerical problems. It is observed that the new methods of the families are equally competitive with the well known special cases of the families.