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This paper discusses an efficient implementation of the generation of orderconditions for the construction of exponential integrators like exponentialsplitting and Magnus-type methods in the computer algebra system Maple. At thecore of this implementation is a new algorithm for the computation ofcoefficients of words in the formal expansion of the local error of theintegrator. The underlying theoretical background including an analysis of thestructure of the local error is briefly reviewed. As an application thecoefficients of all 8th order self-adjoint commutator-free Magnus-typeintegrators involving the minimum number of 8 exponentials are computed.

An Algorithm for Computing Coefficients of Words in Expressions  Involving Exponentials and its Application to the Construction of Exponential  Integrators