A family of fourteenth-order convergent iterative methods for solving nonlinear equations (Q463211)

Summary: We present a family of fourteenth-order convergent iterative methods for solving nonlinear equations involving a specific step which when combined with any two-step iterative method raises the convergence order by \(n+10\), if \(n\) is the order of convergence of the two-step iterative method. This new class include four evaluations of function and one evaluation of the first derivative per iteration. Therefore, the efficiency index of this family is \(14^{1/5} = 1.695218203\). Several numerical examples are given to show that the new methods of this family are comparable with the existing methods.