Study of Local Convergence and Dynamics of a King-Like Two-Step Method with Applications

Abstract

<jats:p>In this paper, we present the local results of the convergence of the two-step King-like method to approximate the solution of nonlinear equations. In this study, we only apply conditions to the first derivative, because we only need this condition to guarantee convergence. As a result, the applicability of the method is expanded. We also use different convergence planes to show family behavior. Finally, the new results are used to solve some applications related to chemistry.</jats:p>