Local Convergence of Parameter Based Derivative Free Continuation Method for the Solution of Non-linear Equations

Abstract

This paper's major purpose is to evaluate the local convergence of the parameter-based sixth- and seventh-order continuation iterative approach for solving nonlinear equations in R. This analysis assumes that the Fréchet derivative of the first order satisfies the Lipschitz continuity condition. Under these circumstances, we explore convergence analysis in order to investigate the existence and uniqueness region for the solution of our proposed strategies. Thus, we also offered the theoretical concept of the radii of convergence balls for the proposed approach. By determining the radii of the convergence balls and solving many numerical problems, we can verify the significance of our convergence study.