We introduce a general format of numerical ODE-solvers which include many of the recently
proposed exponential integrators. We derive a general order theory for these schemes in
terms of B-series and bicolored rooted trees. To ease the construction of specific schemes
we generalize an idea of Zennaro [{\em {Math. Comp.,}} 46 (1986), pp. 119--133] and define
natural continuous extensions in the context of exponential integrators. This leads to a
relatively easy derivation of some of the most popular recently proposed schemes. The …

We introduce a general format of numerical ODE-solvers which include many of the recently
proposed exponential integrators. We derive a general order theory for these schemes in
terms of B-series and bicoloured rooted trees. To ease the construction of specific schemes
we generalise an idea of Zennaro and define Natural Continuous Extensions in the context
of exponential integrators. This leads to a relatively easy derivation of some of the most
popular recently proposed schemes. The general format of schemes considered here makes …