Composite Fourth Order Newton Type Method for Simple Root

Abstract

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.

Keywords:

• Nonlinear Equations
• Newton Type Methods
• Composite Schemes
• Third Order Convergence
• Fourth Order Convergence
• Simple Root
• Taylor Series

Acknowledgement

The author expresses his sincere gratitude to the Director, SERC, for the permission to publish this paper. The author also acknowledges Dr. K. Balaji Rao, SERC, for his constant support and encouragement.