Ball convergence for a three-step one parameter efficient method in banach space under generalized conditions

Abstract:

A local convergence analysis for an eighth-order convergent method is given in order to approximate a locally unique solution of a nonlinear equation for Banach space valued operators. In contrast to the earlier studies using hypotheses up to the seventh Fréchet-derivative, we only use hypotheses on the first-order Fréchet-derivative and Lipschitz constants. Hence, we not only expand the applicability of these methods but also proposed the computable radius of convergence of these methods. Finally, numerical examples demonstrate that our results apply to solve nonlinear equations but results in earlier studies cannot apply.

Año de publicación:

2019

Keywords:

• Iterative method
• Order of convergence
• Banach space
• Lipschitz constant
• local convergence

Fuente:

scopus