Page 146 - Excel for Scientists and Engineers: Numerical Methods
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CHAPTER 6 DIFFERENTIATION I23
Concerning the Choice of Ax
for the Finite-Difference Method
In preceding sections, the x + Ax used for the calculation of the derivatives
was calculated by multiplying x by 1.00000001. Thus Ax is a "scaled" increment.
An alternative approach would have been to use a constant Ax of, e.g.,
0.0000000 1. Either approach has its advantages and disadvantages.
The constant-increment method eliminates the need to handle the case of x = 0
separately. However, the method fails when x is very large, e.g., 10'. The
scaled-increment method handles a wide range of x values, but fails in some
special cases, such as for sin x when x = 1000.
You should be aware of these limitations when using the dydx and d2ydx2
custom functions.
