Discretisation by common sense

Comparing these chords with the actual tangent, it will be clear that the central difference formula, Eq. 3.12, is the most satisfactory on average (it is possible to draw three points where it it is not the best). Any of the above three formulae can be used in digital simulation. 

For the second derivative, we note that this means derivative of the first derivative or rate of change of slope, at. We have two slopes about P - the forward and backward difference first derivatives - and it 

One problem with all these discretisation formulae is that they provide absolutely no information about possible errors. Often, this may be academic - we usually dry-run our serious simulations on systems that have known solutions, to be reasonably sure they are working - but it may be of interest. 

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