A bell-shaped or B-spline u = 0(x) interpolates the data

(a) Find the explicit formula for the natural 5- spline and plot its graph.
(b) Show that 0(x) also satisfies the homogeneous clamped boundary conditions u'(-2) = u´(2) = 0.
(c) Show that 0(x) also satisfies the periodic boundary conditions. Thus, for this particular interpolation problem, the natural, clamped, and periodic splines happen to coincide.

Transcribed Image Text:

B(-2) = 0. B(-1) = 1. B(0) = 4. B(1) = 1, B(2) = 0.