New Root-Finding Methods for Nonlinear Equations

Abstract

In this paper we present three new methods of order four using an accelerating generator that generates root-finding methods of arbitrary order of convergence, based on existing third-order multiple root-finding methods free from the third derivative. The first method requires two-function and three-derivative evaluation per step, and two other methods require one-function and two-derivative evaluation per step. Numerical examples suggest that these methods are competitive to other fourth-order methods for multiple roots and have a higher informational efficiency than the known methods of the same order.