In this paper, a new family of higher order Steffensen-type methods for solving nonlinear equations are constructed. ?It is proved that these methods have the convergence order of four to seven. The seventh, sixth and fifth order derivative-free methods only use four evaluations of the function per iteration, whereas the fourth-order derivative-free method is achieved with three function evaluations. The theory is supported by numerical examples comparing the existing methods with the new higher-order Steffensen-type methods presented.
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