Finite difference end conditions and semi-cardinal interpolation with quintic B-splines

For quintic spline interpolation on a uniform grid, we formulate a class of end conditions in terms of homogeneous finite differences of B-spline coefficients. The analysis of the resulting schemes, including their approximation order, is based on the model of semi-cardinal interpolation at the set of non-negative integers. Numerical results are also presented to illustrate the implementation on a finite grid.