An Algorithm Derivative-Free to Improve the Steffensen-Type Methods

Solving equations of the form H(x)=0 is one most faced problem in mathematics and other science fields such as chemistry or physics. This kind cannot be solved without use iterative methods. The Steffensen-type methods, defined using divided differences are derivative free, usually considered to solve these problems when H a non-differentiable operator due its accuracy efficiency. However, general, accessibility methods small. main interest this paper improve set starting points that converge roots applying those So, by means predictor–corrector process we can accessibility. For this, predictor process, symmetric differences, with good then, corrector method, consider Center-Steffensen method quadratic convergence. In addition, dynamical studies presented show, an experimental way, also improves region Moreover, analyze semilocal convergence proposed two cases: differentiable non-differentiable. Summing up, present effective alternative for Newton’s operators, where applied. theoretical results illustrated numerical experiments.