An Efficient Cubically Convergent Two-Point Newton Method

A numerical procedure fo r solving non-linear equations is presented which is a modification of the Two Point Newton Method developed by the author earlier. It is shown that the method presented here has a third order convergence. The modified procedure incorporates computation of the x value for an intermediate point using the original Two Point Newton Method. The derivative of the intermediate point is also estimated through linear extrapolat ion of the first derivatives of the previous two points of the iteration while the functional value for the intermediate point is obtained by applying trapezoidal rule on the first derivatives between the nearest point and the intermediate point. The computational efficiency of the proposed method is h igh since the method requires evaluation of two functions per iterationonly while attaining a third order convergence. Examples have been presented in this paper that show the application of the method and comparison of the rate o f convergence of the method with the Newton Method as well as withthe previously developed Two point Newton Method.