mkdiff.cwp.lib

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MKDIFF - Make an n-th order DIFFerentiator via Taylor's series method.

mkdiff		make discrete Taylor series approximation to n'th derivative.

Function Prototype:
void mkdiff (int n, float a, float h, int l, int m, float d[]);

Input:
n		order of desired derivative (n>=0 && n<=m-l is required)
a		fractional distance from integer sampling index (see notes)
h		sampling interval
l		sampling index of first coefficient (see notes below)
m		sampling index of last coefficient (see notes below)

Output:
d		array[m-l+1] of coefficients for n'th order differentiator

Notes:
The abscissae x of a sampled function f(x) can always be expressed as
x = (j+a)*h, where j is an integer, a is a fraction, and h is the
sampling interval.  To approximate the n'th order derivative fn(x)
of the sampled function f(x) at x = (j+a)*h, use the m-l+1 coefficients
in the output array d[] as follows:

	fn(x) = d[0]*f(j-l) + d[1]*f(j-l-1) +...+ d[m-l]*f(j-m)

i.e., convolve the coefficients in d with the samples in f.

m-l+1 (the number of coefficients) must not be greater than the
NCMAX parameter specified below.

For best approximations,
when n is even, use a = 0.0, l = -m
when n is odd, use a = 0.5, l = -m-1

Author:  Dave Hale, Colorado School of Mines, 06/02/89