IMPROVED CONVERGENCE ANALYSIS FOR THE KURCHATOV METHOD

Abstract

We present a new convergence analysis for the Kurchatov method using our new idea of restricted convergence domains in order to solve nonlinear equations in a Banach space setting. The sufficient convergence conditions are weaker than in earlier studies. Hence, we extend the applicability of this method. Moreover, our radius of convergence is larger leading to a wider choice of initial guesses and fewer iterations to achieve a desired error tolerance. Numerical examples are also provided showing the advantages of our approach over earlier work.