Resumen de Extended convergence ball for an efficient eighth order method using only the first derivative

Ioannis K. Argyros, Debasis Sharma, Christopher I. Argyros, Sanjaya Kumar Parhi, Shanta Kumari Sunanda

• We develop an extended convergence ball for an efficient eighth order method to obtain numerical solutions of Banach space valued nonlinear models. Convergence of this algorithm has previously been shown using assumptions up to the ninth derivative. However, in our convergence theorem, we use only the first derivative. As a consequence, in contrast to previous ideas, the results on calculable error bounds, convergence radius and uniqueness zone for the solution are provided. Furthermore, this scheme is applied to several complex polynomials and related attraction basins are displayed. The results of numerical tests are presented and compared with the earlier technique. We arrive at the conclusion that the suggested analysis produces much larger convergence radii in all tests. Hence, we expand the convergence domain of this iterative formula.