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

Abstract

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.