Functionally-fitted methods are generalizations of collocation techniques to integrate an equation
exactly if its solution is a linear combination of a chosen set of basis functions. When these basis functions
are chosen as the power functions, we recover classical algebraic collocation methods. This paper shows that
functionally-fitted methods can be derived with less restrictive conditions than previously stated in the
literature, and that other related results can be derived in a much more elegant way. The novelty in our
approach is to fully retain the collocation framework without reverting back into derivations based on
cumbersome Taylor series expansions. ?? Springer Science + Business Media B.V. 2006.
