>   (v[x-1] - v[x]) + (v[x] - v[x+1]) =

Oh, and just for clarity, you should probably write that as:

(v[x+1]-v[x]) - (v[x]-v[x-1])

rather than:

(v[x-1]-v[x]) - (v[x]-v[x+1])

In your case it makes no difference because you are differentiating twice, 
but in general differentials are usually defined to be positive if v[x] 
increases with x.

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