I'm preparing for my exams next week, and I'm making exercises as a preparation. Now, I'm asked to derive the following formula using Richardson Extrapolation based on the centered difference formula:
Find this formula: $f'(x) = \frac{1}{12h}*(f(x - 2h) - 8f(x - h) + 8f(x + h) - f(x + 2h))$
The centered difference formula is this one:
$f'(x) \approx \frac{f(x + h) - f(x - h)}{2h}$
I'm given a solution telling me the following:
$F(h) = f'(x) + a_1*h^2 + O(h^4) \\ F(2h) = f'(x) + a_1*(2h)^2+O(h^4) \\ 4*F(h) - F(2h) = 3 * f'(x) + O(h^4)$
Now I'm not sure where this last equation comes from?