Discretization and the variational principle

Hi,

I'm trying to get a proper FD discretizion of the radial Schroedinger
equation [-1/2 * d^2/dr^2+V(r)] * f(r) = E * f(r) with f(0)=0 on a
_non-uniform_ mesh. Using a 3-point approximation for the differential
operator works quite well but I expect to get better results if I discretize
the underlying variational principle, i.e. the Lagrangian (as proposed in
S.E. Koonin's "Computational Physics").

I already found some examples for this procedure in literature but only for
grids with equi-distant collocation points. Do you know any papers or books
where the whole discretization is done explicitely for non-uniform grids?
Unfortunately my own efforts were not very successful so far (the results
were worse than the direct discretization) ...

Greetings, Stefan



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