New Nonlinear Four-Step Method for y'' = f(t, y)

In this paper, a study is made on the possibility of developing a nonlinear four-step method based on contraharmonic mean. The study is done since the four-step methods always give higher order than popular methods like Numerov and classical Runge-Kutta methods. A detailed study of consistency, stability, convergence and interval of periodicity has been done to convince ourselves of using this new method. The numerical results shows that the method is more accurate than the existing one.