New Methods of the Fourth Order for Finding Multiple Roots of Nonlinear Equation

In this paper we present three new methods of order four using anaccelerating generator that generates root-finding methods of arbitrary order ofconvergence, based on existing third-order multiple root-finding methods free fromthe third derivative. The first method requires two-function and three-derivativeevaluation per step, and two other methods require one-function and two-derivativeevaluation per step. Numerical examples suggest that these methods are competitiveto other fourth-order methods for multiple roots and have a higher informationalefficiency than the known methods of the same order