CHEBYSHEV-KURCHATOV-TYPE METHODS FOR SOLVING EQUATIONS WITH NON-DIFFERENTIABLE OPERATORS

Abstract

We introduce a new derivative free family of difference iterative methods for solving nonlinear equations with non-differentiable operators in a Banach space setting. This family is obtained as a combination of Chebyshev's and Kurchatov's method, and is shown to be faster than the corresponding one using the Chebyshev's or Kurchatov's methods. Numerical examples validate our semilocal convergence results.