  In a series of papers the present authors and their coworkers have developed
a family of algebraic techniques to solve a number of problems in the theory of
discrete or continuous dynamical systems and to analyze numerical integrators.
Given a specific problem, those techniques construct an abstract, {\em
universal} version of it which is solved algebraically; then, the results are
tranferred to the original problem with the help of a suitable morphism. In
earlier contributions, the abstract problem is formulated either in the dual of
the shuffle Hopf algebra or in the dual of the Connes-Kreimer Hopf algebra. In
the present contribution we extend these techniques to more general Hopf
algebras, which in some cases lead to more efficient computations.
