Abstract
We study the local convergence of a family of fifth and sixth convergence order derivative free methods for solving Banach space valued nonlinear models. Earlier results used hypotheses up to the seventh derivative to show convergence. However, we only use the first divided difference of order one as well as the first derivative in our analysis. We also provide computable radius of convergence, error estimates, and uniqueness of the solution results not given in earlier studies. Hence, we expand the applicability of these methods. The dynamical analysis of the discussed family is also presented. Numerical experiments complete this article.
Highlights
One of the major goals of this study is to arrive at an estimated solution x∗ of the equation
This research allows for the visualization of the set of starting values that converge to a solution or other locations
We study the dynamical the class (34) applied on a two degree complex polynomial H (z) : C → C defined by H (z) = (z − s1)(z − s2)
Summary
One of the major goals of this study is to arrive at an estimated solution x∗ of the equation. Many authors [17,18,19,20,21,22,23,24,25,26,27] deduced the local results for different iterative processes In these studies, essential outcomes, like measurements on error estimates, calculable convergence radii, and improved utility of highly efficient iterative algorithms have been derived. Argyros and George [28] studied the local convergence analysis of a seventh order iterative algorithm without inverses of derivatives. This method can be written, as follows.
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