# Forward difference formula extrapolation

1. Jan 24, 2006

### stunner5000pt

the forward difference formula can be expressed as
$$f'(x_{0}) = \frac{1}{h} [f(x_{0} + h) - f(x_{0})] - \frac{h}{2} f''(x_{0}) - \frac{h^2}{6} f'''(x_{0}) + O(h^3)$$

use extrapolation to derivae an O(h^3) formula for f'(x0)

would i be using the taylor expansion to get the answer here? I knwo this is somehow related to Richardson's extrapolation.
$$N_{j} (h) = N_{j-1} (h) (\frac{h}{2}) + \frac{N_{j-1}(h/2) - N_{j-1} (h)}{4^{j-1} -1}$$