Creating a new two-step recursive memory method with eight-order based on Kung and Traub's method.
DOI:
https://doi.org/10.22199/issn.0717-6279-2020-05-0072Keywords:
Nonlinear equations, Simple roots, Computational order of convergence, Weight function, Recursive method with memoryAbstract
We are devoted to the study of an iterative recursive Traub-Steffensen like method for approximating the simple roots of a nonlinear equation. Using the recursive technique, the R-order of convergence is increased from 4 to 8 without any new function evaluations, which means 100% improvement of the order of the convergence. The theoretical study of the convergence rate is investigated and demonstrated. A few nonlinear problems are presented to justify the theoretical study.
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