Ball convergence for eighth order method

Abstract

Consider the problem of approximating a locally unique solution x of the nonlinear equation F(x) = 0, (21.1) where F is a Fréchet-differentiable operator defined on a convex subset D of a Banach space X with values in a Banach space Y. The equation (21.1) covers wide range of problems in classical analysis and applications [1-30]. Closed form solutions of these nonlinear equations exist only for few special cases which may not be of much practical value. Therefore solutions of these nonlinear equations (21.1) are approximated by iterative methods.