The construction of optimal fourth-order iterative schemes for solving univariate nonlinear equations is discussed. Per iteration, the methods consist of three evaluations of the function and they are free from any derivative calculation which property is so fruitful in engineering problems. We analytically show the fourth-order convergence. Numerical examples are considered to confirm the applicability and to justify the rapid convergence of the novel iterative algorithms.
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Fazlollah Soleymani (2011) studied this question.
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