Novel Computational Iterative Methods with Optimal Order for Nonlinear Equations

Abstract EN

This paper contributes a very general class of two-point iterative methods without memory for solving nonlinear equations.

The class of methods is developed using weight function approach.

Per iteration, each method of the class includes two evaluations of the function and one of its first-order derivative.

The analytical study of the main theorem is presented in detail to show the fourth order of convergence.

Furthermore, it is discussed that many of the existing fourth-order methods without memory are members from this developed class.

Finally, numerical examples are taken into account to manifest the accuracy of the derived methods.