Adams-like techniques for zero-finder methods

Two families of zero-finding iterative methods for nonlinear equations are presented. We derive them solving an initial value problem using Adams-like multistep techniques. Namely, Adams methods have been used to solve the problem that consists in a differential equation in what appears the inverse function of the one which zero will be computed and the condition given by the value attained by it at the initial approximation. Performing this procedure several methods of different local orders of convergence have been obtained.