An Algorithm for Computing Coefficients of Words in Expressions Involving Exponentials and Its Application to the Construction of Exponential Integrators
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This paper discusses an efficient implementation of the generation of order conditions for the construction of exponential integrators like exponential splitting and Magnus-type methods in the computer algebra system Maple. At the core of this implementation is a new algorithm for the computation of coefficients of words in the formal expansion of the local error of the integrator. The underlying theoretical background including an analysis of the structure of the local error is briefly reviewed. As an application the coefficients of all 8th order self-adjoint commutator-free Magnus-type integrators involving the minimum number of 8 exponentials are computed.
KeywordsSplitting methods Magnus-type integrators Local error Order conditions Computer algebra
This work was supported in part by the Austrian Science Fund (FWF) under grant P30819-N32 and the Vienna Science and Technology Fund (WWTF) under grant MA14–002.