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

  • 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.


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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How to Cite
Al-Turkmani, Z., & Al-Subaihi, I. (2022). A New Family of Optimal Eighth-Order Iterative Scheme for Solving Nonlinear Equations. Journal of Progressive Research in Mathematics, 19(1), 44-53. Retrieved from http://www.scitecresearch.com/journals/index.php/jprm/article/view/2131