Constructing third-order derivative-free iterative methods

Abstract

In this work, we develop nine derivative-free families of iterative methods from the three well-known classical methods: Chebyshev, Halley and Euler iterative methods. Methods of the developed families consist of two steps and they are totally free of derivatives. Convergence analysis shows that the methods of these families are cubically convergent, which is also verified through the computational work. Apart from being totally free of derivatives, numerical comparison demonstrates that the developed methods perform better than the three classical methods.

Keywords:

• iterative methods
• third order
• Newton
• derivative free
• convergence
• nonlinear
• Chebyshev
• Euler
• Cauchy
• Halley

2000 AMS Subject Classifications :

• 41H25
• 65D99

Acknowledgements

We are grateful to the reviewers for the constructive remarks and suggestions that have enhanced our work. We thank Professor D.H. Bailey for guiding us to properly use the ARPREC high-precision library.