Extended convergence for a fifth-order novel scheme free from derivatives

[EN] The objective in this paper is the expansion of the utilization for a fifth convergence order scheme without derivatives for finding solutions of Banach space valued equations. Conditions of the first order divided difference of the operator involved are only imposed. In this way the use of the scheme is expanded, since in earlier articles the derivatives until order four that do appear in the iterative method are required for setting convergence. Our technique also provides bounds on error distances as well as information about the location of the solutions not given in earlier works. Experiments with concrete problems complete this study.