HA(N,IA,IB)= ( H(N,IA+1,IB) - H(N,IA-1,IB) ) / 2
At the edges of the lattice, the derivative are evaluated as the difference between the value at the end-point and the nearest neighbour.
For evaluating dH/dB, a little more caution has to be used, since a very big derivative occurs locally when a heavy quark turns on. One finds the differences between the values at the given point and points adjacent to it on either side, and chooses the smaller of the two as the derivative at the point. The derivatives for points at the edges are computed as was done for derivatives of A.
The second derivative of the parton distribution with respect to both A and B is then calculated. The methods used are similar to those described above. In the interior of the lattice, the two differences HABL and HABR are calculated, corresponding to the second derivative d**2H/dAdB depending on whether the point to the left of B is taken into account or the one to the right of B. The smaller of the two is chosen as the actual value of the second derivative. The values at the edges of the lattice are taken as the difference between values at the end-point and the nearest neighbours.
anandam@darkwing.uoregon.edu