ملخص المقالة :
Generalized solution on Neumann problem of the fourth order ordinary differentialequation in space $W^2_\alpha(0,b)$ has been discussed, we obtain the condition on B.V.P when thesolution is in classical form. Formulation of Quintic Spline Function has been derived and theconsistency relations are given.Numerical method,based on Quintic spline approximation hasbeen developed. Spline solution of the given problem has been considered for a certain valueof $\alpha$. Error analysis of the spline method is given and it has been tested by an example.
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