Extended ball convergence for a seventh order derivative free class of algorithms for nonlinear equations

Abstract

In the earlier work, expensive Taylor formula and conditions on derivatives up to the eighthorder have been utilized to establish the convergence of a derivative free class of seventh orderiterative algorithms. Moreover, no error distances or results on uniqueness of the solution weregiven. In this study, extended ball convergence analysis is derived for this class by imposingconditions on the first derivative. Additionally, we offer error distances and convergence radiustogether with the region of uniqueness for the solution. Therefore, we enlarge the practicalutility of these algorithms. Also, convergence regions of a specific member of this class are displayedfor solving complex polynomial equations. At the end, standard numerical applicationsare provided to illustrate the efficacy of our theoretical findings.