A sixth-order iterative method free from derivative for solving multiple roots of a nonlinear equation

Abstract

We discuss an iterative method, based on a three-step Newton-like method, to nd a multiple root of a nonlinear equation. To avoid appearing the derivatives in the method, we approximate them with a central dierence and divided dierence. We show analytically that the method is of order six. We verify the theoretical result on relevant numerical problems and compare the behavior of the proposed method with some existing methods.