On semilocal convergence of two step Kurchatov method

ABSTRACT

In this article we present a new semilocal convergence analysis for the two step Kurchatov method by using recurrence relations under Lipschitz type conditions on first-order divided difference operator. The main advantage of this iterative method is that it does not require to evaluate any Fréchet derivative but it includes extra parameters in the first-order divided difference in order to ensure a good approximation to the first derivative in each iteration. The detailed study of the domain of parameters of the method has been carried out and the applicability of the proposed convergence analysis is illustrated by solving some numerical examples. It has been concluded that the present method converges more rapidly than the one step Kurchatov method and two step Secant method.

KEYWORDS:

• Nonlinear equations
• Kurchatov's method
• semilocal convergence
• recurrence relations
• domain of parameters

2010 AMS SUBJECT CLASSIFICATIONS:

• 65H10
• 65J15

Disclosure statement

No potential conflict of interest was reported by the authors.