Three-point approximation
 

Hi there,

I would like to use a three point approximation as a boundary conditions, but having an unequal space grid, so far I only found information about the central differences while using those grids.

The very known relation is:
f'(x) = [ -3f(x) + 4f(x+h) -f(x+2h) ] / (2*h)

But how does the relation change for an unequal space grid (instead of h, I have h1 and h2) ?

Thank you very much !

3 point formula with enequal spacing
 

Hi Artmis,

The solution is quite simple. Fit a parabola that interpolates f(x), f(x+h1) and f(x+h2) at x, x+h1, and x+h2. Call this interpolated parabola fp(x). Then, fp'(x) is the expression you are looking for. The procedure is the same for higher orders as well.

Best,
Sam