Local convergence for a quadrature based third-order method using only the first derivative

Abstract

We extend the applicability of a method for approximating a locally unique solution of a nonlinear equation. The convergence analysis in earlier work was based on Taylor expansions and hypotheses reaching up to the second derivative of the function involved, although only the first derivative appears in the method. In this study, we use only hypotheses on the first derivative of the involved function. Numerical examples are also presented in this study. 2019, Tsing Hua University. All rights reserved.