A New Family of Optimal Eighth-Order Iterative Scheme for Solving Nonlinear Equations

Z. Al-Turkmani; Ibrahim Ahmed Al-Subaihi

Z. Al-Turkmani Department of Civil Engineer, Collage of Engineering, University of Prince Mugrin, Saudi Arabia
Ibrahim Ahmed Al-Subaihi Department of General Studies, University of Prince Mugrin, Saudi Arabia

Keywords: Convergence order; Efficiency index; Iterative methods; Nonlinear equations; Optimal eighth-order.

Abstract

The objective of this manuscript is to introduce a new family of optimal eight-order iterative methods for computing the numerical zeros of a nonlinear univariate equation that is not dependent on the second derivative. The family was designed to enhance the order of convergence by merging Bawazir’s method and Newton’s method as a third step. To demonstrate the performance of the offered scheme, assorted numerical comparisons have been investigated. In addition, the efficiency index of the new family is 1.6818.

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