An automatic symbolic-numeric Taylor series ODE solver

One of the basic techniques in every mathematician's toolkit is the Taylor series representation of functions. It is of such fundamental importance and it is so well understood that its use is often a first choice in numerical analysis. This faith has not, unfortunately, been transferred to the design of computer algorithms. Approximation by use of Taylor series methods is inherently partly a symbolic process and partly numeric. This aspect has often, with reason, been regarded as a major hindrance in algorithm design. Whilst attempts have been made in the past to build a consistent set of programs for the symbolic and numeric paradigms, these have been necessarily multi-stage processes. Using current technology it has at last become possible to integrate these two concepts and build an automatic adaptive symbolic-numeric algorithm within a uniform framework which can hide the internal workings behind a modern interface.