Following the computational algorithm developed by Bruma & Cuperman (1996) for the calculation of horizontal derivatives in problems of the type studied here, we use a ``flexible" fourteen-grid-point formulation designed to achieve optimal accuracy.
1. Denote by 
the coordinates of a set of equidistant grid points along
the x-axis and by
..,
,..
the values of the function F at the corresponding grid points;
here F stands for either
or
.
Also, use the notation
. 
, where 
represents the equidistant grid size.
2. Concerning the meaning of subscripts used:
(a) the subscripts 
define
a ``moving" set of fifteen grid-point numbers;
(b) the subscripts 
indicate the order of the moving-set along the x-axis,
starting at 
(where i = 1 ) and ending at
3. At a point
, the optimal value of the
derivative
is obtained through a systematic
investigation leading to the minimization of the relative
error involved.
This procedure leads to one of the
following two possibilities: (a) use of a symmetric fourteen-point
formula, with seven points on each side of the
point 
or, (b) use of a non-symmetric
variable-number-of-terms-formula 
at the left or at the right of 
.
For illustration, in the case (a), one has
For the case (b)
A complete description on the general algorithm, including the criteria for the selection of the formulas for the horizontal derivations is given in Bruma & Cuperman (1996).
