An O(h⁶ ) Quinltic Spline Interpolation for Quintic Spline Collocation Method

An quintic spline interpolate to a function in $C^{10}$[a, b] and its O($h^6$) error behavior are presented when its fourth derivative satisfies some kind of end conditions. The O($h^6$) relations between its derivatives up to fourth order and the m-th derivatives of the given function are also given at the nodes.