Combination of Newton-Halley-Chebyshev Iterative Methods Without Second Derivatives

Abstract

This article discusses the modification of three step iteration method to solve nonlinear equations f(x)=0. The new iterative method is formed from a combination of Newton, Halley, and Chebyshev methods. To reduce the number of evaluation functions, some derivatives in this method are estimated by Taylor polynomials. Using analysis of convergence we show that the new method has the order of convergence fourteen. Numerical computation shows that the new method are comparable to other methods discussed.

A New Second Derivative Free Iterative Method of Fifth Order of Convergence and Its Applications

“…Many researchers have employed several techniques in order to avoid these problems. There is a vast literature on how to avoid the calculation of second derivative in an iterative methods as one can find in ( [5], [8], [9], [10], [11], [12], [13]).…”