The number of conditions to be satisfied by the operators K and P in symplectic integrators with processing, given by e P e -hK e -P , is determined for a Hamiltonian of the form H= A+ B. The conditions for K are explicitly written up to order six and used to obtain more efficient methods with fewer evaluations per step than other symplectic integrators. Special cases in which the number of conditions for the kernel is drastically reduced are also studied. It is shown that the kernel completely determines the optimal method one can obtain by processing.
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Blanes et al. (1999) studied this question.
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