Overshoot

With the number you have given then any interpolation scheme will do the same, these systems don't like sharp corners. Even a very higher order polynomial, or Fourier approach (I've yet to write these but will), will have local overshot.

Therefore what you have to do is locally force conformity, it'll require a little bit of experimentation, but try this:

N=12 1 2 2.1 2.2 3 4 5 6 7 8 9 10 0 8.75 8.75 8.75 8.75 8.75 8.75 8.75 8.75 8.75 8.75 8.75 1:10

I've bolded the two extra terms (I hope you see these at 2.1 and 2.2).