A class of derivative free schemes for solving nondifferentiable Banach space valued equations

Abstract

In this study, we have extended the applicability of two-step methods with non-differentiable parts for solving nonlinear equations defined in Banach spaces. The convergence analysis uses conditions weaker than the ones in earlier studies. Other advantages include computable a priori error distances based on generalized conditions, an extended region of convergence as well as a better knowledge of the isolation for the solutions. The earlier results use assumptions on the eighth derivative of the main operator. But there are no derivatives on the schemes. Moreover, the previous results cannot be used for nondifferentiable equations although the schemes may converge. Numerical examples validate further our approach. © The Author(s), under exclusive licence to The Forum D’Analystes 2024.