On the convergence of a new fourth-order method for finding a zero of a derivative

On the basis of Wang's method, a new fourth-order method for finding a zero of a derivative was presented. Under the hypotheses that the third and fourth order derivatives of nonlinear function were bounded, the local convergence of a new fourth-order method was studied. The error estimate, the order of convergence, and uniqueness of the solution were also discussed. In particular, Herzberger's matrix method was used to obtain the convergence order of the new method to four. By comparing the new method with Wang's method and the same order method, numerical illustrations showed that the new method has a higher order of convergence and accuracy.