From the abstract, "simulations of such systems are usually done on digital computers, which are able to compute with finite sequences of rational numbers only."
Not at all! Digital computers can use computable reals which are defined as any function from a rational value (the error bound) to a rational value which is within the supplied error-bounds from the true value. Do not mistake this for computing in the rationals, these functions which perform the described task are the computable real numbers. There are countable-infinity many of these functions, one for each computable real. For instance, note that you can always compare two rationals for equality, but you can't always compare two computable reals for equality, just like reals.
Not at all! Digital computers can use computable reals which are defined as any function from a rational value (the error bound) to a rational value which is within the supplied error-bounds from the true value. Do not mistake this for computing in the rationals, these functions which perform the described task are the computable real numbers. There are countable-infinity many of these functions, one for each computable real. For instance, note that you can always compare two rationals for equality, but you can't always compare two computable reals for equality, just like reals.
Hans Boehm (of Boehm garbage collector fame) has been working on this for a long time, here is a recent paper on it: https://dl.acm.org/doi/pdf/10.1145/3385412.3386037