section 5， we present a set of nurical tegrations for the outer five ps that spans ± 5 x 1010 yrsection 6 we also discs the long-ter stability of the pary otion and its possible cae
2 description of the nurical tegrations
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23 nurical thod
we utilize a send-order wisdo–hon syplectic ap as our a tegration thod (wisdo ≈ap;ap;ap; hon 1991; koa， yoshida ≈ap;ap;ap; nakai 1991) with a special start-up procedure to reduce the truncation error of angle variables，‘war start’(saha ≈ap;ap;ap; treae 1992， 1994)
the stepsize for the nurical tegrations is 8 d throughout all tegrations of the ne ps (n±1，2，3)， which is about 1/11 of the orbital period of the nerost p (rcury) as for the deteration of stepsize， w
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