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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.

PSEUDO SPLINE METHOD FOR SOLVING CERTAIN SECOND ORDER INITIAL VALUE PROBLEM OF ORDINARY DIFFERENTIAL EQUATION