In this paper, new set of low order schemes for solving certain second order initial value problem of differential equations directly are derived. From the general method of deriving a spline function, schemes based on interpo- lation and collocation were derived. In the process of derivation we observed that it is possible to obtain the discrete scheme from the continuous scheme by collocating at a given point. Also from the process of derivation the Adams'-Stormer formula were recovered for the explicit scheme and the Cowell formula for the implicit scheme.