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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 efficiency index 5 1 3 ≈ 1.70998, 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. c ©2016 All rights reserved.

A new Householders method free from second derivatives for solving nonlinear equations and polynomiography