A new family of optimal fourth-order iterative methods for nonlinear equations

Abstract

A new two-parameter family of fourth-order iterative methods for the numerical solution of nonlinear equations of the form f(x)=0 has been introduced and their convergence analysis have been performed. The new methods in the family are optimal in the sense of Kung–Traub conjecture. Numerical tests which are made to support the theoretical results also show that our new family of optimal fourth order methods perform well and in many cases some members of the family are superior to other well-known and recent fourth order optimal methods in the literature.