The split integration symplectic method.

r 0 H H H + = where 0 H is the pure harmonic part and r H is the remaining part. This splitting, incorporated in the second order generalized leapfrog scheme, gives the following approximation for the solution operator of the Hamiltonian system ( ) ( ) ( ) 0 0 r 0 0 t H 2 t H H 2 t t t | x L exp L t exp L exp | x r r ∆ ∆ ∆ + ∆ ≈ which prescribes how to propagate from one point in the phase space to another. The system is first propagated by H0 for a half integration step, then for a whole step by H1, and finally for another half step by H0. This integration scheme was employed in the development of the SISM, a second order symplectic