Further Development of Jarratt Method for Solving Nonlinear Equations

We present two new families of Jarratt-type methods for solving nonlinear equations. It is proved that the order of convergence of each family member is improved from four to six by the addition of one function evaluation. Per iteration, these new methods require two evaluations of the function and two evaluations of the first-order derivatives. In fact, the efficiency index of these methods is 1.565. Numerical comparisons are made with other existing methods to show the performance of the presented methods.