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

Abstract 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.