A family of Newton-type methods for solving nonlinear equations

Abstract

A family of Newton-type methods free from second and higher order derivatives for solving nonlinear equations is presented. The order of the convergence of this family depends on a function. Under a condition on this function this family converge cubically and by imposing one condition more on this function one can obtain methods of order four. It has been shown that this family covers many of the available iterative methods. From this family two new iterative methods are obtained. Numerical experiments are also included.

Keywords:

• Nonlinear equation
• Newton's method
• Order of convergence
• Iterative methods

Acknowledgements

The author would like to thank the referees for their valuable comments which substantially improved the quality of this paper.

Additional information

Notes on contributors

Davod Khojasteh Salkuyeh

Email: [email protected]