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:
- to calculate numerically the partial derivatives using finite differences and then interpolating them,
- 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.