End conditions for cubic spline interpolation derived from integration

摘要

In the literature, most of the end conditions for spline functions are obtained from conditions imposed on the spline function, its finite differences, or its derivatives near the two endpoints. In this paper a class of end conditions is derived for cubic spline functions by use of integration. These end conditions are given in terms of function values at the knots (data), and give rise to O(h4) spline approximation. Also, it is shown that some of these end conditions have been obtained before from other constraints.