Fudge factors and arbitrary parameters

Closely connected with error cancelling, fudge factors have enjoyed some popularity in digital simulation and to some extent still do so. These are sometimes arbitrary factors thrown in to improve the results and sometimes incorrect derivations of the discretisations. A good example of the first sort is the correction factor used by Prater and Bard (1970) who - to be fair - were not the first. By this means, they were able to simulate a rotating ring-disk system with only 50 time steps and they do warn the reader that, for other 6T, different correction factors may be needed. 

An unintentional fudge factor is found in the usual end-element expression with the box method, as in Eq. 3.9. If we recognise the equivalence of boxes and the concentration point distribution 0, H/2, 3H/2,. .., and apply the Taylor expansion method to it as in Sect. 3.1.4 

The correct discrete expression, Eq. 6.12, has rarely been used (for example, by Hanafey et al, 1978) - most simulators using the box method prefer to use Eq. 3.9. If we recognise CN as an accurate technique when used to simulate the Cottrell experiment, then it confirms the 4/3 factor. This implies that, when using Eq. 3.9, one is (unintentionally) applying a fudge factor of 0.75. It so happens that this makes the result better for the explicit box method but this must again be error cancelling. 

Another quantity can be considered a fudge the J 6T shift that is 

For a X value of 0.4, commonly used, we then get T 0.25T. A similar calculation for the point method gives 6T/nX or 0.86T. In effect, we are starting the simulation not at T 0 but at these (calculable) times. The actual value depends on the simulation technique and the current approximation used. In neither the box- or point case, though, is the starting time equal to i ST. 

---