Fastest Iteration Method for Estimation of Solution of Nonlinear Function f(x)=0 (Bennie's Method)

-There has been a considerate progress and achievement in development of mathematical models and different formulas of which they are used to describe behavior of different systems. Several Numerical methods were used for estimations of fixed points, roots, and series expansion. However in many cases when roots were evaluated using the fixed point method, the number of iteration required to end process by inferring the final answer was very long, sometimes it took more than 1000 iterations inferring the final answer. Fixed point method has been found not to converge in some functions, f (x) =0 thus disclosed failure In this paper we introduced the fastest method of iteration (Bennies iteration) for Estimation of roots of a functions and square roots with zero error-bounds and high convergence speed. Fixed point iteration and slop finding had accelerated the establishment of the algorithm. With this approach mathematicians found easier and straightforward to evaluate roots of a function manually. Moreover the algorithm resolved all problems of which fixed point method found to diverge. In addition to that this paper deduced the newtons method from the proposed Bennies method (scheme).