Composite Fourth Order Newton Type Method for Simple Root

In this paper, first we present a family of cubically convergent schemes with three functions (one function and two first derivatives) evaluation per iteration based on Newton function. Next, based on inverse Newton function, we present another family of cubically convergent schemes with three functions (one function and two first derivatives) evaluation per iteration. Finally, we combine a special case of first family with a special case of second family and propose a composite fourth order scheme. The proposed composite scheme also requires three functions (one function and two first derivatives) evaluation per iteration. Application of the proposed scheme to a system of nonlinear equations is also illustrated.