Some modifications of King’s family with optimal eighth order of convergence
2012
Soleymani, F. | Vanani, S Karimi | Khan, M. | Sharifi, M.
Kung and Traub (1974) [4] conjectured that an iteration method without memory based on n+1 evaluations could achieve optimal convergence order 2ⁿ. Hence, based on this conjecture, we derive two optimal three-step eighth-order classes of methods in which there are only four evaluations per full cycle. Analytical proofs of the presented derivative-involved classes are provided. Finally, a number of numerical examples are also proposed to illustrate the accuracy of the contributed methods by comparing with the new existing optimal eighth-order methods without memory in the literature.
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