JR Park,

I understand you expect that someone is able to explain you the difference in deflections 12.5 mm in your hand calculation and 19.8 mm in your model. This is not possible without having details about your model.

But I expect you can have results closed to deflection of 12.5 mm if you model a large number -let's say 11- elements of 18,895 mm (representing the span), add a middle point on each span and consider proper supports.
Looking to the deflection of the middle span of your model,you can expect to have the deflection closed to 12.5 mm, but not this value for marginal and intermediate elements. In fact it is what Michael suggested you previously.

Theoretically, for an infinite continuous beam with equal spans, you have no rotation on supports due to the symmetry; each half of span is balanced by the half of span beyond adjacent support and eventually, in this situation, in which part would be possible a rotation on support, clockwise or counterclockwise? or no rotation?
For this case, because you have no rotation on supports the deflection formula should be identical with "fixed end" one span (even you have just rests as supports).

Because you haven't an "an infinite continuous beam", nobody can guess (but one can hand calculate-there are several methods well known in the old school, however useless in practice for our days) the actual deflection on spans of a continuous beam.

It is true that the "old practice" was to approximate something between simple supported case (when the rotation on supports is maximum) and "fixed end" case (when the rotation on supports is zero). The numerical coefficients for deflection are 5/384 for the first case and 1/384 for the last one. With no math reasons, the engineers assumed a coefficient as arithmetic mean of those coefficients; you can find in books a "generic formula" for deflection with a coefficient of 3/384= 1/128. But this is just a reasonable approach useful to dimension spans, you cannot use it to check a software. For your case, it seems there is a coefficient as 1.58/384 and this is due to some rotation on supports.