Modified Newton's Methods with Seventh or Eighth -Order Convergence

In this paper, we consider a modification of the Newton's method which produce iterative method with fourth-order of convergence have been proposed in [4] and obtain new methods with ( seventh or eighth )-order convergence for solving non-linear equations. A general error analysis providing the higher order of convergence is given. Per iteration the new methods require one additional evaluation of the function. Numerical examples are also included the performance of the new methods