I'd like to pay attention to an article J, B. van den Berg and J.-P. Lessard, Notices of the AMS, October 2015, p. 1057-1063. We know numerous applications of CASes to algebra. The authors present such applications to dynamics. It would be interesting and useful to obtain opinions of Maple experts on this topic.
Here is its introduction:
"Nonlinear dynamics shape the world around us, from the harmonious movements of celestial bod-
ies, via the swirling motions in fluid flows, to the complicated biochemistry in the living cell.
Mathematically these beautiful phenomena are modeled by nonlinear dynamical systems, mainly
in the form of ordinary differential equations (ODEs), partial differential equations (PDEs) and
delay differential equations (DDEs). The presence of nonlinearities severely complicates the mathe-
matical analysis of these dynamical systems, and the difficulties are even greater for PDEs and DDEs,
which are naturally defined on infinite-dimensional function spaces. With the availability of powerful
computers and sophisticated software, numerical simulations have quickly become the primary tool
to study the models. However, while the pace of progress increases, one may ask: just how reliable
are our computations? Even for finite-dimensional ODEs, this question naturally arises if the system
under study is chaotic, as small differences in initial conditions (such as those due to rounding
errors in numerical computations) yield wildly diverging outcomes. These issues have motivated
the development of the field of rigorous numerics in dynamics"