Author(s)

Osama Y. Ababneh

Department of Mathematics, Zarqa University, Zarqa, Jordan.

In a recent paper, Noor and Khan [M. Aslam Noor, & W. A. Khan, (2012) New Iterative Methods for Solving Nonlinear Equation by Using Homotopy Perturbation Method, Applied Mathematics and Computation, 219, 3565-3574], suggested a fourth-order method for solving nonlinear equations. Per iteration in this method requires two evaluations of the function and two of its first derivatives; therefore, the efficiency index is 1.41421 as Newton’s method. In this paper, we modified this method and obtained a family of iterative methods for appropriate and suitable choice of the parameter. It should be noted that per iteration for the new methods requires two evaluations of the function and one evaluation of its first derivatives, so its efficiency index equals to 1.5874. Analysis of convergence shows that the methods are fourth-order. Several numerical examples are given to illustrate the performance of the presented methods.

Newton’s Method, Fourth-Order Convergence, Third-Order Convergence, Non-Linear Equations, Root-Finding, Iterative Method

Ababneh, O. (2016) New Fourth Order Iterative Methods Second Derivative Free. Journal of Applied Mathematics and Physics, 4, 519-523. doi: 10.4236/jamp.2016.43058.