Abstract
A three-step class of iterative methods without memory for approximating the simple roots of single valued nonlinear equations is suggested. Theoretical proof shows that it has eighth-order convergence by consuming three evaluations of the function and one of its first order derivative per full iteration. One method of the class is generalized for finding the multiple zeros when the multiplicity of the roots are not known. The analytical results are supported through numerical works to put on show the efficacy of the new methods. Moreover, the basins of attraction for some of the high order methods in the complex plane will be given.
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