[gmx-users] cubic spline and continuous derivatives

[Floris Buelens]

Hello,

The gromacs manual states that for cubic spline interpolation of potential 
energy and forces, "V and V’ are continuous, while V” is the first discontinuous 
derivative." This makes sense to me as there is a unique solution for parameters 
A2 and A3 if V and V' to the left and right are given for each piecewise 
polynomial.
However the definition of a cubic spline seems to be for a set of functions 
continous up to the second derivative. Is the cubic spline formulation used 
somehow unorthodox in this sense? I'm using a similar scheme in a slightly 
different context, is it strictly correct to refer to it as cubic spline 
interpolation?
Thanks,

Floris