On the development and extensions of some classes of optimal three-point iterations for solving nonlinear equations

Abstract

We develop a new families of optimal eight--order methods for solving nonlinear equations. We also extend some classes of optimal methods for any suitable choice of iteration parameter. Such development and extension was made using sufficient convergence conditions given in [14]. Numerical examples are considered to check the convergence order of new families and extensions of some well-known methods.

Keywords

• nonlinear equations in R
• order of convergence
• multipoint methods