HP35s and numerical differentiation

[Thomas Klemm]

(10-05-2014 04:43 PM)Eddie W. Shore Wrote:  \[\frac{f(x-2h)-8f(x-h)+8f(x+h)-f(x+2h)}{12h}\]

This expression can be transformed into:
\[\frac{4\frac{f(x+h)-f(x-h)}{2\cdot h}-\frac{f(x+2h)-f(x-2h)}{2\cdot 2h}}{4-1}\]

Now we can see that this is the 1st step of the Richardson extrapolation for \(\frac{f(x+h)-f(x-h)}{2\cdot h}\):



This can be extended similar to Romberg's method.


Cheers
Thomas