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

Abstract

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.

Keywords

• king-like iterative methods
• local convergence
• lipschitz conditions
• dynamics