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).

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