Semilocal convergence by using recurrence relations for fifth-order method in Banach spaces

In this paper, a semilocal convergence result in Banach spaces of an efficient fifth-order method is analyzed. Recurrence relations are used in order to prove this convergence, and some a priori error bounds are found. This scheme is finally used to estimate the solution of an integral equation and so, the theoretical results are numerically checked. We use this example to show the better efficiency of the current method compared with other existing ones, including Newton's scheme.This research was supported by Ministerio de Ciencia y Tecnologia MTM2011-28636-C02-{01,02}.Cordero Barbero, A.; Hernandez-Veron, MA.; Romero, N.; Torregrosa Sánchez, JR. (2015). Semilocal convergence by using recurrence relations for fifth-order method in Banach spaces. Journal of Computational and Applied Mathematics. 273:205-213. https://doi.org/10.1016/j.cam.2014.06.00820521327