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Composite Fourth Order Newton Type Method for Simple Root

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

Document Type: Research Article

DOI: https://doi.org/10.1080/15502280802069889

Affiliations: Structural Engineering Research Center, Chennai, India

Publication date: 2008-07-01

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