Modified Newton Type Methods with Higher Order Convergence

Abstract

Inspired by a recent result of McDougall and Wortherspoon, we obtain new iterative methods for solving nonlinear equations. Also we derive certain hybrid methods these methods and the standard secant method. The resulting methods turn out to be of higher order of convergence and are more efficient than the existing ones. The methods are compared with some of the recent existing methods.

Key words and phrases. Newton method, secant method, predictor-corrector method, nonlinear equation, order of convergence.

1991 Mathematics Subject Classification. 65H05