Abstract
The objective of this paper is to develop new class of optimal iterative methods that do not need any derivative evaluations for solving nonlinear equations. Those new methods consist of an approximation of the eighth order and require four function evaluations per iteration which support the Kung-Traub assumption on optimal order for without memory schemes. Lastly, to show those new methods' performance and effectiveness, they are compared numerically with other similar methods in high-precision computation.
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