[aurelian15]

Yes, thank you for the clarification, my statement is ambiguous.

I meant to say that the theory required to describe a computation on a practical analogue computer (that is noisy) is no different than the theory required to describe the same computation on a digital computer, because they essentially are both discrete systems.

However, as you point out (at least as I understand your first paragraph), when we analyse/build systems on an abstract level we assume (often as a simplification) that they are ideal continuous systems.