A new Househölder's method free from second derivatives for solving nonlinear equations and polynomiography

Abstract

In this paper, we describe the new Husehölder's method free from second derivatives for solving nonlinear equations. The new Husehölder's method has convergence of order five and effciency index 5⅓ ≈70998, which converges faster than the Newton's method, the Halley's method and the Husehölder's method. The comparison table demonstrate the faster convergence of our method. Polynomiography via the new Husehölder's method is also presented.