A Review of an Eleventh Order of Chebyshev–Halley Type Method for Solving Nonlinear Equations

Abstract

In this paper, we present a new eleventh order method for solving nonlinear equations numerically. This method is based on the methods of Chebyshev and Halley methods and requires five function evaluations (two function calculations, two first derivative calculations, and a second derivative calculation). Therefore, the efficiency index of this method is √11 5 = 1,615. The numerical comparisons made also show that the method of this article has good efficiency.