I have a series of points extracted from numerical simulations. I also recently discovered the amazing power of finite differences. Nevertheless, I was used to estimate my derivatives from the analytic expression of the interpolation between my points.

My question: Is it better, in the sense more correct:

  1. to calculate numerically the partial derivatives using finite differences and then interpolating them,
  2. or to interpolate my points and derivate analytically the interpolation?

I feel like way 1 is better for my sets. I also imagine that interpolation or trend curves may have non-physical variations, e.g. Runge oscillations in the case of polynomial interpolation. Such oscillations would lead way 2 to being completely non-sense.

Of course I did extensive testings on my sets of points, but I'd like a more rigorous answer than I'm able to give.

  • $\begingroup$ I am not sure what interpolation methods and finite difference methods you are focusing on. Finite difference methods usually coincide with the result from some interpolation methods but require less computation. $\endgroup$ – Tunococ Jul 15 '13 at 8:29

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