Abstract
A local convergence analysis for a generalization of a family of Steffensen-type iterative methods with three frozen steps is presented for solving nonlinear equations. From the use of three classical divided difference operators, we study four families of iterative methods with optimal local order of convergence. Then, new variants of the family of iterative methods is constructed, where a study of the computational efficiency is carried out. Moreover, the semilocal convergence for these families is also studied. Finally, an application of nonlinear integral equations of mixed Hammerstein type is presented, where multiple precision and a stopping criterion are implemented without using any known root. In addition, a study, where we compare orders, efficiencies and elapsed times of the methods suggested, supports the theoretical results obtained.
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