Accurate estimates for the fundamental solutions of discrete boundary value problems

It is investigated how the solutions of a discretized ODE can be related to solutions of the ODE, by using a perturbation analysis based on boundary value formulations. In particular it is indicated how one can find estimates for discrete modes that correspond to certain continuous modes. These estimates are fairly sharp in a relative sense as is shown by some examples. As a consequence one can deduce that certain properties of the one solution space like a dichotomy, carry over to the other.