A penta-parametric family of fifteenth-order multipoint methods for nonlinear equations

A penta-parametric family of four-step multipoint iterative methods of order fifteen for nonlinear algebraic equations are developed and their convergence properties are established. The efficiency indices are all found to be 15^1/5 ≈ 1.71877, better than 14^1/5 ≈ 1.69522 of a family of fourteenth-order methods suggested by Neta 9]. Numerical examples are demonstrated to verify the developed theory.