New Family of Combined Iterative Methods for Solving Nonlinear Equations

In this paper, a new family of combined iterative methods for the solution of nonlinear equations is presented.The new family of methods is based on Newton's method and the family of sixth-order iterative methods developed by Chun. Per iteration the new methods require three evaluations of the function and two evaluations of its first derivative. Numerical tests show that it takes less number of iterations than Newton's method and some methods with third-order convergence. It is found that it only adds evaluation of the function at another point but its convergence order will be increased (p+1)-order above the original level.