A Class of Two-Step Newton s Methods with Accelerated Third Order Convergence

In this work we propose an improvement to the popular Newton s method based on the contra-harmonic mean while using quadrature rule derived from a Ostrowski-Grauss type inequality developed in . The order of convergence of this method for solving non-linear equations which have simple roots is shown to be three. Computer Algebra Systems (CAS), such as MAPLE 18 package, can be used successfully to take over the lengthy and tedious computations in deriving the asymptotic error of convergence. Furthermore, numerical experiments are made to show the efficiency and robustness of the suggested method.