Order conditions for exponential integrators

This paper provides an algebraic framework for the generation of order conditions for the construction of exponential integrators like splitting and Magnus-type methods for the numerical solution of evolution equations. The generation of order conditions is based on an analysis of the structure of the leading local error term of such an integrator, and on a new algorithm for the computation of coefficients of words in expressions involving exponentials. As an application a new 8th order commutator-free Magnus-type integrator involving only 8 exponentials is derived.