A New Uniform Fourth Order One-Third Step Continuous Block Method for the Direct Solutions of y′′ = f (x, y, y′)

In this study, we applied the approach of collocation and interpolation to develop a new fourth order continuous one-third hybrid block method for the solutions of general second order initial value problems of ordinary differential equations. Three discrete schemes were derived from the continuous schemes. The discrete method was analyzed based on the properties of linear multistep methods and the method is found to be zero-stable, consistent and convergent. We reported an improved performance of the new method over the existing methods in the literature by solving four numerical examples and the approximate solutions obtained confirmed the superiority of our new developed scheme when compared with some latest existing approaches.