Local Convergence of a Seventh Order Derivative-Free Method for Solving Nonlinear Equations in Banach Spaces

This manuscript presents the study of local convergence of a seventh order derivative free method in Banach spaces. Earlier study showed the convergence of method using derivatives up to fifth order and only in the n-dimensional Euclidean space. Domain of convergence, computable error bounds and uniqueness of the solution were not studied earlier, thereby limiting the applicability of the method. In present study we focus on these problems and extended the method in more general setting of a Banach space using hypothesis only on the first derivative. Numerical examples are presented to verify the theoretical results.