The second half of a Hermite step is again a Taylor series development, this time to a higher order than in the predictor step, even though this is not obvious from the way it is written. We refer to the discussion in the beginning of chapter 6, where the Taylor series character of the corrector step is made explicit. Here is the code:
![\begin{Code}[nbody\_sh1.C: correct\_step]
\small\verbatiminput{chap8/nbody_sh1.C.correct_step} \end{Code}](img722.png)